双稳态随机共振系统的输出的性能衡量
|
摘要
随机共振现象是非线性动力学系统中的一种反直观的现象，当一个非线性动力学系统受到一个随机力(噪声)的激励，也就是系统输入具有一个连续的频谱，系统和输入的随机激励之间会产生一种协同作用，使得系统输出的性能有所提高，这一现象被称为随机共振。在过去的二十多年里，随机共振现象受到广泛的关注，这一现象也在最初的双稳态动力学系统之外的其他许多系统中被发现。随着研究的深入，在被用来解释许多不同领域的自然现象之外，随机共振现象开始获得了一些应用，而随机共振在信号处理中的应用则是其中倍受关注的一个。
但是到目前为止，随机共振在信号处理中的应用的研究还只是局限在很小的范围内，主要原因是以前大量的研究工作都从调节噪声强度出发。随着参数调节随机共振(PSR)概念的提出，随机共振在信号处理中的应用有着很大拓展的空间，本文就主要研究几个目前随机共振在信号处理中应用时经常碰到的问题，其中包括阱内随机共振现象对多频模拟信号处理的应用、双稳态系统输出的波形畸变的消除及其他后处理、适用于多频信号的输出性能衡量指标、二进制数字信号输入情况下的系统输出的性能衡量，并将所得的结果应用到了一个自然界的噪声——海洋噪声背景下的信号检测中，这些研究对于随机共振理论的进一步发展及其在非线性信号处理中的应用具有重要的意义。
在对最近发现的一个很特别的现象——阱内随机共振现象进行研究中，我们发现阱内随机共振现象更有利于对多频信号的处理。同时，对于模拟信号输入的情况，大部分已有的结果都是集中在单频信号上的，这主要是由于双稳态系统的输出有严重的波形畸变。对于单频信号可以很好的利用频谱特性进行检测，或者通过带通滤波器进行处理，但是对于多频信号，没有很简单的方法。本文在仔细地分析了双稳态系统输出的线性特性的础上提出了一个简单的反演方法，并发展了相关的后处理操作。进一步地，我们还给出了阱内随机共振情形下，经过后处理操作，多频信号输入时系统输出性能的衡量指标。
对于二进制数字信号输入的情况，已有颇多研究结果，本文是在引入了系统响应速度的基础上，具体结合二进制信号的检测形式，对上述情况下的系统输出的统计性态进行了详细的研究，并最终得到了一个优于以前结果的系统输出误码率公式，给系统参数的选取提供了更好的依据。动态误码率公式，以及上面提到的多频信号输入时系统输出性能的衡量指标，已经被成功的应用在了我们对海洋噪声背景下的信号检测的研究中。
随机共振在信号处理中的应用的研究是一个跨学科的工作，本文还是主要着眼于随机共振现象的机理和在应用中的一些关键性制约因素，与信号处理领域的结合还不够紧密，随机共振如何更好地与信号处理相结合还需要大量进一步的工作。
Stochastic resonance (SR) is a counterintuitive phenomenon of nonlinear dynamic systems wherein the noise (stochastic force) plays a constructive role. This phenomenon has then attracted much attention in the past two decades, and it has been observed that SR can occur in a wide variety of systems. With the development of SR, it has far been found to account for many natural phenomena and shown a large number of applications in different areas of technology, among which signal processing via stochastic resonance is a worth subject to be concerned.
For a long time, SR was described as a phenomenon wherein the response of a nonlinear system to a weak periodic input signal is optimized by the presence of a particular level of noise. However, this description has served to limit the application of SR to signal processing. Parameter-tuning stochastic resonance (PSR) is a more realistic way to handle the phenomenon of SR in a broad sense. Based on the theory of PSR, some key problems of using SR in signal processing are studied, these issues include: the application of intrawell SR in multi-frequency analog signal processing, recovery of the waveform distortion caused by the bistable system and other post treatments, measure of system performance with multi-frequency analog digital input and measurement of system performance of binary digital input. The results are used in signal detecting under the background of the real sea noise. It is important for the development of SR theory and its application in nonlinear signal processing.
With the work on a recently proposed phenomenon of SR ?the intrawell SR, we found that intrawell SR is a more effective way to process multi-frequency input. Most of the literatures considering analog input are focused on simple harmonic input, because the output waveform from a bistable system is greatly distorted. As for single harmonic input, the output information can be easily retrieved by some typical methods, such as frequency analysis and a bandpass filter. But when treating a multi-frequency analog signal, there is not a simple method. Based on the analysis of waveform distortion caused by bistable systems, a recovery formula is proposed, and some other post treatments are considered as a whole job. Then a measure on intrawell SR with multi-frequency input is obtained.
There are many results on SR with binary digital input. As an extension of our previous works, a dynamic bit error rate (DBER) is obtained in this thesis. The DBER is a more accuracy measure to be used in SR with binary input, because the evaluation of system output is considered more detailedly with the concept of system response speed. The measure mentioned above, and the DBER have been used in the work of signal detection under the background of real sea noise.
Using stochastic resonance in signal processing is a subject of more then two field of learning, only some of the key points of SR and the limitations in application are considered in this thesis. In order to join SR with signal processing more closely, further work needs to be done on the subject of using stochastic resonance in signal processing.
但是到目前为止，随机共振在信号处理中的应用的研究还只是局限在很小的范围内，主要原因是以前大量的研究工作都从调节噪声强度出发。随着参数调节随机共振(PSR)概念的提出，随机共振在信号处理中的应用有着很大拓展的空间，本文就主要研究几个目前随机共振在信号处理中应用时经常碰到的问题，其中包括阱内随机共振现象对多频模拟信号处理的应用、双稳态系统输出的波形畸变的消除及其他后处理、适用于多频信号的输出性能衡量指标、二进制数字信号输入情况下的系统输出的性能衡量，并将所得的结果应用到了一个自然界的噪声——海洋噪声背景下的信号检测中，这些研究对于随机共振理论的进一步发展及其在非线性信号处理中的应用具有重要的意义。
在对最近发现的一个很特别的现象——阱内随机共振现象进行研究中，我们发现阱内随机共振现象更有利于对多频信号的处理。同时，对于模拟信号输入的情况，大部分已有的结果都是集中在单频信号上的，这主要是由于双稳态系统的输出有严重的波形畸变。对于单频信号可以很好的利用频谱特性进行检测，或者通过带通滤波器进行处理，但是对于多频信号，没有很简单的方法。本文在仔细地分析了双稳态系统输出的线性特性的础上提出了一个简单的反演方法，并发展了相关的后处理操作。进一步地，我们还给出了阱内随机共振情形下，经过后处理操作，多频信号输入时系统输出性能的衡量指标。
对于二进制数字信号输入的情况，已有颇多研究结果，本文是在引入了系统响应速度的基础上，具体结合二进制信号的检测形式，对上述情况下的系统输出的统计性态进行了详细的研究，并最终得到了一个优于以前结果的系统输出误码率公式，给系统参数的选取提供了更好的依据。动态误码率公式，以及上面提到的多频信号输入时系统输出性能的衡量指标，已经被成功的应用在了我们对海洋噪声背景下的信号检测的研究中。
随机共振在信号处理中的应用的研究是一个跨学科的工作，本文还是主要着眼于随机共振现象的机理和在应用中的一些关键性制约因素，与信号处理领域的结合还不够紧密，随机共振如何更好地与信号处理相结合还需要大量进一步的工作。
Stochastic resonance (SR) is a counterintuitive phenomenon of nonlinear dynamic systems wherein the noise (stochastic force) plays a constructive role. This phenomenon has then attracted much attention in the past two decades, and it has been observed that SR can occur in a wide variety of systems. With the development of SR, it has far been found to account for many natural phenomena and shown a large number of applications in different areas of technology, among which signal processing via stochastic resonance is a worth subject to be concerned.
For a long time, SR was described as a phenomenon wherein the response of a nonlinear system to a weak periodic input signal is optimized by the presence of a particular level of noise. However, this description has served to limit the application of SR to signal processing. Parameter-tuning stochastic resonance (PSR) is a more realistic way to handle the phenomenon of SR in a broad sense. Based on the theory of PSR, some key problems of using SR in signal processing are studied, these issues include: the application of intrawell SR in multi-frequency analog signal processing, recovery of the waveform distortion caused by the bistable system and other post treatments, measure of system performance with multi-frequency analog digital input and measurement of system performance of binary digital input. The results are used in signal detecting under the background of the real sea noise. It is important for the development of SR theory and its application in nonlinear signal processing.
With the work on a recently proposed phenomenon of SR ?the intrawell SR, we found that intrawell SR is a more effective way to process multi-frequency input. Most of the literatures considering analog input are focused on simple harmonic input, because the output waveform from a bistable system is greatly distorted. As for single harmonic input, the output information can be easily retrieved by some typical methods, such as frequency analysis and a bandpass filter. But when treating a multi-frequency analog signal, there is not a simple method. Based on the analysis of waveform distortion caused by bistable systems, a recovery formula is proposed, and some other post treatments are considered as a whole job. Then a measure on intrawell SR with multi-frequency input is obtained.
There are many results on SR with binary digital input. As an extension of our previous works, a dynamic bit error rate (DBER) is obtained in this thesis. The DBER is a more accuracy measure to be used in SR with binary input, because the evaluation of system output is considered more detailedly with the concept of system response speed. The measure mentioned above, and the DBER have been used in the work of signal detection under the background of real sea noise.
Using stochastic resonance in signal processing is a subject of more then two field of learning, only some of the key points of SR and the limitations in application are considered in this thesis. In order to join SR with signal processing more closely, further work needs to be done on the subject of using stochastic resonance in signal processing.
引文
1． R. Benzi, A. Sutera, & A. Vulpiani, "The mechanism of stochastic resonance," J. Phys. A, Vol. 14(11) , pp. L453-L457, 1981．
2． R. Benzi, G. Parisi, & A. Vulpiani. "Stochastic resonance in climatic change," Tellus, Vol. 34, pp. 10-16, 1982．
3． L. Gammaitoni, P. Hanggi, P. Jung, et al. "Stochastic resonance," Rev. Mod. Phys., Vol. 70(1) , pp. 223-285, 1998．
4． S. Mitaim & B. Kosko, "Adaptive stochastic resonance," Pro. IEEE, Vol. 86(11) , pp. 2152-2183,1998．
5． S. Fauve & F. Heslot, "Stochastic resonance in a bistable system," Phys. Lett., Vol. 97A (1-2) , pp. 5-7, 1983．
6． B. McNamara, K. Wiesenfeld, & R. Roy, "Observation of stochastic resonance in a ring laser," Phys. Rev. Lett., Vol. 60, p. 2626,1988; "Theory of stochastic resonace," Phys. Rev. A, Vol. 39(9) , pp. 4854-4868, 1989．
7． K. Wiesenfeld & F. Jaramillo, "Minireview of stochastic resonance," Chaos, Vol. 8(3) , pp. 539-548, 1998．
8． K. Wiesenfeld & F. Moss, "Stochastic resonance and the benefits of noise: from ice ages to crayfish and SQUIDs," Nat., Vol. 373, pp. 33-36, 1995．
9． F. Moss, D. Pierson & D. O'Gorman, "Stochastic resonance: Tutorial and update," Int. J. Bifur. & Chaos, Vol. 4(6) , pp. 1383-1397,1994．
10． A.R. Bulsara & L. Gammaitoni, "Tuning in to noise," Phys. Today, Vol. 49(3) , pp. 39-45,1996．
11． M.I. Dykman, "What can stochastic resonance do?" Nature, Vol. 391, p. 344, 1998．
12． D.G Luchinsky, R. Mannella, P.V.E. McClintock, et al. "Stochastic resonance in electrical circuits-Ⅰ: Conventional stochastic resonance," IEEE Trans. Cir. & Sys.-Analog and digital signal processing, Vol. 40(9) , pp. 1205-1214,1999．
13． D.G Luchinsky, R. Mannella, P.V.E. McClintock, et al. "Stochastic resonance in electrical circuits-Ⅱ: Nonconventional stochastic resonance," IEEE Trans. Cir. & Sys.-Analog and digital signal processing, Vol. 40(9) , pp. 1215-1224,1999．
14． B. McNamara & K. Wiesenfeld, "Theory of stochastic resonance," Phys. Rev. A., Vol. 39(9) , pp. 4854-4869, 1989．
15． L. Gammaitoni, F. Marchesoni, E. Menichella-Saetta et al. "Stochastic resonance in bistable systems," Phys. Rev. Lett., Vol. 62(4) , p. 349, 1989．
16． M.I. Dykman, R. Mannella, P.V.E. McClintock, et al. "Comment on 'Stochastic resonance in bistable systems'," preceding Comment, Phys. Rev. Lett., Vol. 65, p. 2606, 1990．
17． M.I. Dykman, D.G Luchinsky, et al., "Stochastic resonance: Linear response theory and giant nonlinearity," J. Stat. Phys., Vol.70 (1/2) , pp. 463-479,1993．
18． M.I. Dykman, R. Mannella, P.V.E. McClintock, et al, "Giant nonlinearity in the low-frequency response of a fluctuating bistable system," Phys. Rev. E, Vol. 47(3) , pp. 1629-1632, 1993． "Spectral density fluctuations of a double-well Duffing oscillator driven by white noise," Phys. Rev. A, Vol. 37(4) , pp. 1303-1312, 1988．
19． T. Zhou & F. Moss, "Analog simulations of stochastic resonance," Phys. Rev. A, Vol. 41(8) , pp. 4255-4264, 1990．
20． M.H. Choi, R.F. Fox & P. Jung, "Quantifying stochastic resonance in bistable systems: response vs residence-time distribution functions," Phys. Rev. E, Vol. 57(6) , pp. 6335-6344, 1998．
21． L. Gammaitoni, F. Marchesoni, & S. Santucci, "Stochastic Resonance as a Bona Fide resonance", Phys. Rev. Lett., Vol. 74, p. 1052, 1995．
22． G Giacomelli, F. Maria & I. Rabbiosi, "Stochastic and bona-fide resonance: an experimental investigation," Phys. Rev. Lett., Vol. 82(4) , pp. 675-678, 1999．
23． P. Hanggi & P.V.E. McClintock, "Bistablity driven by colored noise: Theory and experiment," Phys. Rev. A, Vol. 32(1) , pp. 695-698,1985．
24． P. Jung & P. Hanggi, "Stochastic nonlinear dynamic modulated by external periodic forces," Europhys. Lett., Vol. 8(6) , pp. 505-510, 1989．
25． R. F. Fox, "Stochastic resonance in a double well," Phys. Rev. A, Vol. 39(8) , pp. 4148-4153,1989．
26． P. Jung & P. Hanggi, "Amplification of small signals via stochastic resonance," Phys. Rev. A, Vol. 44(12) , pp. 8032-8042, 1991．
27． Hu G, G Nicolis & C. Nicolis, "Periodically forced Fokker-Planck equation and stochastic resonance," Phys. Rev. A, Vol. 42(4) , pp. 2030-2041, 1990．
28． JJ. Collins, C.C. Chow, & T.T. Imhoff, "Aperiod stochastic resonance in excitable systems," Phys. Rev. E, Vol. 52(4) , pp. R3321-3324, 1995．
29． J.J. Collins, C.C. Chow, A.C. Capela, et al. "Aperiod stochastic resonance," Phys. Rev. E, Vol. 54(5) , pp. 5575-5584, 1996．
30． C. Heneghan, C.C. Chow, J.J.Collins, et al. "Information measures quantifying aperiod stochastic resonance," Phys. Rev. E, Vol. 54(3) , R2228-2231,1996．
31． J.J. Collins, T.T. Imhoff, & P. Grigg, "Noise-enhanced tactile sensation," Nature, Vol. 383, p. 770, 1996．
32． A.R. Bulsara & A. Zador, "Threshold detection of wideband signal: A noise-induced maximum in the mutual information," Phys. Raw. E, Vol. 54(3) , pp. R2185-2188, 1996．
33． A. Neiman, B. Shulgin, V. Anishchenko, et al. "Dynamical entropies applied to stochastic resonance," Phys. Rev. Lett, Vol. 76(23) , pp. 4299-4302, 1996．
34． Hu G, Gong D., Wen X., et al., "Stochastic resonance in a nonlinear system driven by an apeoridic force," Phys. Rev. A, Vol. 46(6) , pp. 3250-3254,1992．
35． M. Stemmler, "A single spike suffices: the simplest form of stochastic resonance in model neurons," Network: Comput. Neural Sys, Vol. 7, pp. 687-716, 1996．
36． L. Glass, "Synchronization and rhythmic processes in physiology," Nature, Vol. 410, pp. 277-284, 2001．
37． F. Chapeau-Blondeau. "Noise-enhanced capacity via stochastic resonance in an asymmetric binary channel," Phys. Rev. E, Vol. 55(2) , pp. 2016-2019, 1997．
38． X. Godivier, J. Rojas-Varela, & F. Chapeau-Blondeau, "Noise-assisted signal transmission via stochastic resonance in a diode non-linearity," Electronics Letters, Vol. 33(20) , pp. 1666-1668, 1997．
39． X. Godivier & F. Chapeau-Blondeau, "Noise-assisted signal transmission in a nonlinear electronic comparator: Experiment and theory," Signal Processing, Vol. 56, pp. 293-303, 1997．
40． F. Chapeau-Blondeau & X. Godivier, "Theory of stochastic resonance in signal transmission by static nonlinear systems," Phys. Rev. E, Vol. 55(2) , pp. 1478-1495, 1997．
41． J.W.C. Robinson & D.E. Asraf, "Information-theoretic distance measures and a generalization of stochastic resonance," Phys. Rev. E, Vol. 81(14) , pp. 2850-2853,1998．
42． X. Godivier & F. Chapeau-Blondeau, "Stochastic resonance in the information capacity of a nonlinear dynamic systems," Phys. Rev. E, Vol. 8(3) , pp. 581-589, 1998．
43． M.E. Inchiosa & A.R. Bulsara, "dc signal detection via dynamical asymmetry in a nonlinear device," Phys. Rev. E, Vol. 58(1) , pp. 115-127, 1998．
44． F. Chapeau-Blondeau, "Stochastic resonance and optimal detection of pulse trains by threshold devices," Dig. Sig. Proc., Vol. 9, pp. 162-177,1999．
45． S. Zozor & P.O. Amblard, "Stochastic resonance in discrete time nonlinear AR(1) Models," IEEE Trans, on Sig. Proc., Vol. 47(1) , pp. 108-121, 1999．
46． F. Chapeau-Blondeau, "Periodic and aperiodic stochastic resonance with output signal-to-noise ratio
exceeding that at the input," Int. J. Bifurcation and Chaos, Vol. 9(1) , pp. 267-272,1999．
47． D.F Russell, L.A. Wilkens, & Frank Moss, "Use of behavioral stochastic resonance by paddle fish for feeding," Nature, Vol. 402, pp. 291-293,1999．
48． J.E. levin & J.P. Miller, "Broadband neural encoding in the cricket cereal sensory system enhanced by stochastic resonance," Nature, Vol. 380(14) , pp. 165-168, 1996．
49． S. Barbay, G Giacomelli & F. Marin, "Experimental evidence of binary aperiod stochastic resonance," Phys. Rev, Lett., Vol. 85(22) , pp. 4652-4655, 2000．
50． I. Goychuk & P. Hanggi, "Stochastic resonance in ion channels characterized by information theory," Phys. Rev. E, Vol. 61(4) , pp. 4272-4280,2000．
51． M.N. Lorenzo, V. Perez-Mufluzuri & V. Perez-Villar, "Noise performance of a synchronization scheme through compound chaotic signal," Int. J. Bifurcation & Chaos, Vol. 10(12) , pp. 2863-2870, 2000．
52． R.P. Morse & P. Roper, "Enhanced coding in a cohlear-implant model using additive noise: Aperiod stochastic resonance with tuning," Phys. Rev. E, Vol. 61(5) , pp. 5683-5692,2000．
53． EL Naschie MS, Gebeshuber IC, A.V. Holden & D. Petracchi, eds. "Stochastic resonance in biological systems," Chaos, Solitons & Fractals, Vol. 11, 2000．
54． T. Wellens & A. Buchleither, "Bistability and stochastic resonance in an open quantum system," Phys. Lett. A, Vol. 268, pp. 131-149,2001．
55． H.E. Plesser & T. Geisel, "Signal processing by means of noise," NEUROCOMPUTING, Vol. 38, pp. 307-312,2001．
56． M. Rudolph & A. Destexhe, "Correlation detection and resonance in neural systems with distributed noise sources," Phys. Rev. Lett., Vol. 86(16) , pp. 3662-3665,2001．
57． F. Liu & W. Wang, "Frequency sensitivity in nervous systems," Chi. Phys. Lett., Vol. 18(2) , pp. 292-294, 2001．
58． V. Schulter-Frohlinde, Y. Ashkenazy & P. Ch. Ivanov, "Noise effects on the complex patterns of abnormal heartbeats," Phys. Rev. E, Vol. 87(6) , p. 068104,2001．
59． N.G Stocks & R. Mannella, "Generic noise-enhanced coding in neuronal arrays," Phys. Rev. E, Vol. 64(3) , p. 030902, 2001
60． T. Kanamaru & T. Horita, "Theoretical analysis of array-enhanced stochastic resonance in ddiffusively coupled FitzHugh-Nagumo equation," Phys. Rev. E, Vol. 64(3) , p. 031908,2001．
61． L. Schimansky-Geier, J.A. Freund, "Noise induced order: stochastic ewsonance," Int. J. Bifurcation & Chaos, Vol. 8(5) , pp. 869-879,1998．
62． N.G Stocks, "Suprathreshold stochastic resonance in multilevel threshold systems," Phys. Rev. Lett., Vol. 84(11) , pp. 2310-2313,2000．
63． N.G Stocks, "Suprathreshold stochastic resonance: an exact result for uniformly distributed signal and noise," Phys. Lett. A, Vol. 279, pp. 308-312, 2001．
64． JJ. Collins, C.C. Chow & T.T. Imhoff, "Stochastic resonance without tuning," Nat., Vol. 376, pp. 236-239, 1995．
65． J.E. Fletcher, S. Havlin & GH. Weiss, J.Stat. Phys. Vol. 51, p. 215, 1988．
66． J. Masoliver & A. Robinson, "Coherent stochastic resonance," Phys. Rev. E, Vol. 51(5) , pp. 4021-4026, 1995．
67． J.M. Porra, "When coherent stochastic resonance appears," Phys. Rev. E, 55(6) , pp.6533-6539, 1997．
68． A.K. Dhara & T. Mukhopadhyay, "Coherent stochastic resonance in the case of two absorbing boundaries," Phys. Rev. E, Vol. 60(3) , pp. 2727-2736, 1999．
69． P.O. Amblard & S. Zozor, "Cyclostationary and stochastic resonance in threshold devices," Phys. Rev. E, Vol. 59(5) , pp. 5009-5020,1999．
70． S. Mitaim, B. Kosko, "Neural fuzzy stochastic resonance," Systems, Man, and Cybernetics, IEEE International Conference on , Vol. 3 , pp. 2237-2242, 1998．
71． S. Mitaim, B. Kosko, "Adaptive stochastic resonance with fuzzy systems," Fuzzy Information Processing Society-NAFIPS, Conference of the North American, pp. 355-359, 1998．
72． S. Mitaim, B. Kosko, "Adaptive stochastic resonance and fuzzy approximation," Intelligent Control (ISIC), Intelligent Systems and Semiotics (ISAS), Proceedings of the 1998 IEEE International Symposium on, pp. 471-476, 1998．
73． P.Jung, U.Behn, E. Pantazelou & F. Moss, Phys. Rev. A, Vol. 46, p.R 1709, 1992．
74． J.F. Lindner, B.K. Meadows & W.L. Ditto, "Array enhanced stochastic resonance and spatiotemporal synchronization," Phys. Rev. Lett., Vol. 75(1) , pp. 3-6,1995．
75． M.E. Inchiosa & A.R. Bulsara, "Signal detection statistics of stochastic resonators," Phys. Rev. E, Vol. 53(3) , pp. R2021-2024, 1996．
76． T.R. Albert, A.R. Bulsara, G Schmera, et al. "An evaluation of the stochastic resonance phenomenon as a potential tool for signal processing," Signals, Systems and Computers, 1993, Conference Record of The Twenty-Seventh Asilomar Conference on.. Vol. 1, pp. 583-587, 1993
77． Neff, J.D.; Patel, GN.; Meadows, B.K.; DeWeerth, S.P.; Ditto, W.L. "Spatiotemporal dynamics of a stochastic VLSI array," Circuits and Systems, ISCAS '98． Proceedings of the 1998 IEEE International Symposium on, Vol. 3, pp: 542-545．
78． P. Arena, R. Caponetto, L. Fortuna, et al. "Noise-supported wavefronts in cellular neural networks," IEEE Trans. Cir. & Sys.-I: Fundmental theory and Application, Vol. 43(3) , pp. 360-363, 2001．
79． D.E. Postnov & O.V. Sosnovtseva, "Stochastic synchronization of coupled coherence resonance oscillators," Int. J. Bifurcation & Chaos, Vol. 10(11) , pp. 2541-2550, 2000．
80． Zhang Y., Hu G & L. Gammaitoni, "Signal transmission in one-way coupled bistable system: noise effect," Phys. Rev. E, Vol. 58(3) , pp. 2952-56,1998．
81． F. Chapeau-Blondeau & J. Rojas-Varela, "Nonlinear signal propagation enhanced by noise via stochastic resonance," Int. J. Bifurcation & Chaos, Vol. 10(8) , pp. 1951-1959,2000．
82． V. I. Sbitney & M.A. Pustovoit, "Stochastic resonance in 2D coupled map lattice model of field-like neural tissue," Int. J. Bifurcation & Chaos, Vol. 10(8) , pp. 1961-1971, 2000．
83． U. Siewert & L. Schimansky-Geier, "Analytical study of coupled two-state stochastic resonance," Phys. Rev. E, Vol. 58(3) , pp. 2843-2852, 1998．
84． Zhou C., J. Kurths & B. Hu, "Array-enhanced coherence resonance: nontrivial effects of heterogeneity and spatial independence of noise," Phys. Rev. Lett., Vol. 87(9) , p. 098101, 2001．
85． A.A. Zaikin, K. Murali & J. Kurths, "Simple electronic circuit model for doubly stochastic resonance," Phys. Rev. E, Vol. 63(2) , p. 020103, 2001．
86． T. Kanamaru, T. Horita & Y. Okabe, "Theoretical analysis of array-enhanced stochastic resonance in the diffusively coupled FitzHugh-Nagumo equation," Phys. Rev. E, Vol. 64(3) , p. 031908, 2001．
87． N.G Stocks & P. Mannella, "Generic noise-enhanced coding in neural arrays," Phys. Rev. E, Vol. 64(3) , p. 030902,2001．
88． Y. Horikawa, "Coherence resonance with multiple peaks in a coupled FitzHugh-Nagumo model," Phys. Rev. ?Vol. 64(3) , p. 031905,2001．
89． C. Hauptmann, F. Kaiser & C. Eichwals, "Signal transfer and stochastic resonance in copied nonlinear systems," Int. J. Bifurcation & Chaos, Vol. 9(6) , pp. 1159-1167, 2000．
90． G Mato, "Stochastic resonance using noise generated by a neural network," Phys. Rev. E, Vol. 59(3) , pp. 3339-43, 1999．
91． S. Kim, S.H. Park & H.B. Pyo, "Stochastic resonance in coupled oscillator systems with time delay," Phys. Rev. Lett., Vol. 82(8) , pp. 1620-23, 1999．
92． A. Krawiecki, A. Sukiennicki & R.A. Kosinski, "Stochastic resonance and noise-enhanced with spatitemporal periodic signal," Phys. Rev. E, Vol. 62(6) , pp. 7683-89,2000．
93． A.A. Zaikin, J.Kurths & L. Schimansky-Geier, "Doubly stochastic resonance," Phys. Rev. Lett., Vol. 85(2) , pp. 227-231,2000．
94． N. Sungar, J.P. Sharpe & S. Weber, "Stochastic resonance in two-dimensional arrays of copied nonlinear oscillators," Phys. Rev. E, Vol. 62(1) , pp. 1413-15,2000．
95． B. Lindner & L. Schimansky-Geier, "Transmission of noise coded versus additive signal through a neuronal ensemble," Phys. Rev. Lett., Vol. 86(4) , pp. 2934-2937, 2001．
96． T. Kapitaniak, "Stochastic resonance in Chaotically forced systems," Chaos, Solitons & Fractals, Vol. 3(4) , pp. 405-410, 1993．
97． VS. Anishchenko, M.A. Safonova & L.O. Chua, "Stochastic resonance in Chua's circuit," Int. J. Bifurcation & Chaos, Vol. 2(2) , pp. 397-401, 1992． "Stochastic resonance in the nonautonomous Chua's circuit," J. Cir., Sys. & Comp., Vol. 3(2) , pp. 553-578, 1993．
98． O. Calvo, C.R. Mirasso & R. Toral, "Coherence resonance in chaotic electronic circuits," Electronics Lett., Vol. 37(17) , pp. 1062-63,2001．
99． Hu G, L. Pivka& A.L. Zheleznyak, "synchronization of a one-dimensional array of Chua's circuits by feedback control and noise," IEEE Trans. Cir & Sys.-I: Fundamental theory and Application, Vol. 42(10) , pp. 736-40,1995．
100． S. Mizutani, T. Sano & T. Uchiyama, "Numerical studies of resonance in a sinusoidally driven chaotic neuron model and its network," Neural Network, Int. Confer. On, Vol. 2, pp. 663-8, 1997．
101． J.Y. Ko, K. Otsuka & T. Kubota, "Quantum-noise-induced order in lasers placed in chaotic oscillation by frequency-shifted feedback," Phys. Rev. Lett., Vol. 86(18) , pp. 4025-28,2001．
102． S.Matyjaskiewicz, A. Krawiecki, et al., "Stochastic multiresonance in a chaotic map with fractal basins of attraction," Phys. Rev. E, Vol. 63(2) , p. 026215, 2001．
103． GD. VanWiggeren & R. Roy, "Communication with chaotic lasers," Science, Vol. 279, pp. 1198-1200, 1998．
104． V.N. Chizhevsky, R. Vilaseca & R. Corbalan, "Amplification of near-resonant signals via stochastic resonance in a chaotic CO2 laser," Phys. Rev. Lett., Vol. 61(6) , pp. 6500-6505,2000．
105． R.M. Siegel & H.L. Read, "Models of the temporal dynamics of visual processing," J. Stat. Phys., Vol. 70(1/2) , pp. 297-308, 1993．
106． D.R. Chialvo & A.V. Apkarian, "Modulated noisy biological dynamics: three examples,' J. Stat. Phys., Vol. 70(1/2) , pp. 375-390, 1993．
107． M. Misono, T. ohmoto, "Noise-enhanced transmission of information in a bistable system," Phys. Rev. E, Vol. 58(5) , pp. 5602-5607, 1998．
108． M. Riani & E. Simonotto, "Stochastic resonance in the perceptual interpretation of ambiguous figures: A neural network model," Phys. Rev. Lett., Vol. 72(19) , pp. 3120-23,1994．
109． M. Stemmler, M. Usher & E. Niebur, "Interaction in primary visual cortex: A model bridging physiology and psychophysics," Science, Vol. 269, pp. 1877-1880, 1995．
110． T. Yang, "Adaptively optimizing stochastic resonance in visual system," Phys. Lett. A, Vol. 245, pp. 79-86, 1998．
111． J.S. Anderson, I. Lampl, et al., "The contribution of noise to contrast invariance of orientation tuning in cat visual cortex," Science, Vol. 290, pp. 1968-72, 2000．
112． GP. Harmer & D. Abbott, "Motion detection and stochastic resonance in noisy environments,"
Microelectronics J., Vol. 32, pp. 959-967, 2001．
113． T. Ditzinger, M. Stadler, et al., "Noise improve three-dimensional perception: Stochastic resonance and other impacts of noise to the perception of autostereograms," Phys. Rev. E, Vol. 62(2) , pp. 2566-2575, 2000．
114． M. Nafie & A.H.Tewfik, "Low power detection using stochastic resonance," The Thirty-Second Asilomar. Conf. On Signal, System and Computer, 1998．
115． A.S. Asdi & A.H. Tewfik, "Detection of weak signals using adaptive stochastic resonance," Pro. IEEE Int. Conf. OnAcoustics, Speech, and Signal Processing, Detroit, MI, 1995．
116． F. Vaudelle, J. Gazengel, et al., "Stochastic resonance and noise-enhanced transmission of spatial signals in optics: the case of scattering." J. Opt. Soc. Am. B, Vol. 15(11) , pp. 2674-2680, 1998．
117． E. Simonotto, M. Riani, et al., "Visual perception of stochastic resonance," Phys. Rev. Lett., Vol. 78(6) , pp. 1186-1189, 1997．
118． L. Gammaitoni, "Stochastic resonance in multi-threshold systems," Phys. Lett. A, Vol. 208, pp. 313-32, 1995．
119． L. Gammaitoni, "Stochastic resonance and dithering effect in threshold physical systems," Phys. Rev. E, Vol. 52(5) , pp. 4691-4698, 1995．
120． R.A. Wannamaker, S.P. Lipshitz & J. Vanderkoov, "Stochastic resonance as dithering," Phys. Rev. E, Vol. 61(10) , pp. 233-236, 2000．
121． R.A. Wannamaker, S.P. Lipshitz, J. Vanderkoov & J.N. Wright, "A theory of nonsubtractive dither," IEEE Trans. Sig. Proc., Vol. 48(2) , pp. 499-516, 2000．
122． J.F. Blinn, "Quantization error and dithering," IEEE Computer. Graphics & Application, pp. 78-82． July, 1994．
123． Hu G, T. Ditzinger, et al., "Stochastic resonance without external periodic force," Phys. Rev. Lett., Vol. 71(6) , pp. 807-810, 1993．
124． A.S. Pikovsky & J. Kurths, "Coherence resonance in noise-driven excitable system," Phys. Rev. Lett., Vol. 78(5) , pp. 775-778, 1997．
125． S.G Lee, A. Neiman & S. Kim, "Coherence resonance in a Hodgkin-Huxley neuron," Phys. Rev. E, Vol. 57(3) , pp. 3292-3297, 1998．
126． P. Jung, "Stochastic resonance and optimal design of threshold detectors," Phys. Lett. A, Vol. 220, pp. 219-223, 1995．
127． J.M.G Vilar, A. Perez-Madrid and J.M. Rubi, "Stochastic resonance in a dipole", Phy. Rev. E, Vol. 54(6) , pp. 6929-6932, 1997．
128． J.M.G Vilar and J.M. Rubi, "Stochastic Multiresonance", Phy. Rev. Lett., Vol. 78(15) , pp. 2882-2885, 1997．
129． N.G Stocks, N.D. Stein & P.V.E. McClintock, J. Phys. A: Math. Gen., Vol. 25, pp. L1119, 1992． "Stochastic resonance in monostable systems," J. Phys. A: Math. Gen., Vol. 26, pp. L385-390, 1993．
130． J.M.G Vilar & J.M. Rubf, "Divergent signal-noise ratio and stochastic resonance in monostable systems," Phys. Rev. Lett., Vol. 77(4) , pp. 2863-66, 1996．
131． A.N. Grigorenko, S.I. Nikitin & GV. Roschepkin, "Stochastic resonance at higher harmonics in monostable systems," Phys. Rev. E, Vol. 56(5) , pp. R4907-4910, 1997．
132． L. Alfonsi, L. Gammaitoni, S. Santucci, et al. "Intrawell stochastic resonance versus inter-well stochastic resonance," Phys. Rev. E, Vol. 62(1) , pp. 299-302, 2000．
133． K. Wiesenfeld, D. Pierson, "Stochastic resonance on a circle," Phys. Rev. Lett., Vol. 72(14) , pp. 2125-2129, 1994．
134． I.K. Kaufman, D.G Luchinsky, "High-frequency stochastic resonance in SQUIDs," Phys. Lett. A, pp. 219-223, Sep. 1996．
135． F. Moss, A. Bulsara, and M.F. Shlesinger, J. Stat. Phys. Vol. 70(1-2) , 1993; Bulsara A., Moss F., Phys. Rev.
Lett., Vol. 67, pp. 656-659, 1991．
136． J.K. Douglass, L. Wilkens, E. Pantazelou, et al. "Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance," Nature, Vol. 365, pp. 337-340, 1993．
137． D. Nozaki & Y. Yamamoto, "Enhancement of stochastic resonance in a FitzHugh-Nagumo neuronal model driven by colored noise," Phys. Lett., A, Vol. 243, pp. 281-287, 1998．
138． T. Shimokawa, A. Rogel, "Stochastic resonance and spike-timing precision in an ensemble of leaky integrate and fire neuron models," Phys. Rev. E, Vol. 59(3) , pp. 3461-3470,1999．
139． T. Ohira & Y. Sato, "Resonance and delay," Phys. Rev. Lett., Vol. 82(14) , pp. 2811-2815, 1999．
140． V. Galdi, V. Pierro & I.M. Pinto, "Evaluation of stochastic-resonance-based detectors of weak harmonic signals in additive white Gaussian noise," Phys. Rev. E, Vol. 57(6) , pp. 6470-6479,1998．
141． M.C. Eguia, M.I. Rabinovich & H.D. Abarbanel, "Information transmission and recovery in neural communication channels," Phys. Rev. E, Vol. 62(5) , pp. 7111-7122, 2000．
142． V.A. Shneidman, P. Jung & P Hanggi, "Weak-noise limit of stochastic resonance," Phys. Rev. Lett., Vol. 72(17) , pp. 2682-2685,1994．
143． R. Lofstedt & S.N. Coppersmith, "Stochastic resonance: Nonperturbative calculation of power spectra and residence-time distribution," Phys. Rev. E, Vol. 49(6) , pp. 4821-4831, 1994．
144． S. Matyjaskiewicz, A. Krawiecki, "Stochastic multiresonance in a chaotic map with fractal basins of attraction," Phys. Rev. E, Vol. 63(2) , p. 026215, 2001．
145． J.A. Gonzalez, I.I. Reyes & L.E. Guerreo, "Solutions to chaotic and stochastic resonance," Chaos, Vol. 11(1) , pp. 1-15,2001．
146． D.T.W. Chik, Y. Wang & Z.D. Wang, "Stochastic resonance in a Hodgkin-Huley neuron in the absence of external noise," Phys. Rev. E, Vol. 64(2) , p. 021913, 2001．
147． I. Goychuk, "Information transfer with rate-modulated Poisson processes: A simple model for nonstationary stochastic resonance," Phys. Rev. E, Vol. 64(2) , p. 021909, 2001．
148． H.E. Plesser & T. Geisel, "Stochastic resonance in neuron models: Endogenous stimulation revisited,'" Phys. Rev. E, Vol. 63(3) , p. 031916, 2001．
149． MR Carusela, R.P.J. Perazzo & L. Romanelli, "Stochastic resonance memory storage device," Phys. Rev. E, Vol. 64(3) , p. 031101,2001．
150． GP. Harmer & D. Abbott, "Simulation of circuits demonstrating stochastic resonance," Microelectronics J., Vol. 31, pp. 553-559,2000．
151． K. Lerincz, Z. Gingl & L.B. Kiss, "A stochastic resonator is able to greatly improve signal-to-noise," Phys. Lett. A, Vol. 224, pp. 63-67, 1996．
152． F. Chapeau-Blondeau, "Input-output gains for signal in noise in stochastic resonance," Phys. Lett. A, Vol. 232, pp. 41-48, 1997．
153． M.T. Blackwell, "Effect of white and filtered noise on contrast detection thresholds," Vision Res., Vol. 38(2) , pp. 267-280,1998．
154． F. Marchesoni, F. Apostolico, "Color effects in a near-threshold Schmitt trigger," Phys. Rev. E, Vol. 58(6) , pp. 7079-84,1998．
155． J.M.G Vilar & R.V. Sole, "Effects of noise in symmetric two-species competition," Phys. Rev. Lett., Vol. 80(18) , pp. 4099-4102, 1998．
156． A. Fulinski, "Relaxation, noise-induced transitions, and stochastic resonance driven by non-Markovian dichotomic noise", Phy. Rev. E, Vol. 52(4) , pp. 4523-4526, 1995; A.V. Barzykin, K. Seki & F. Shibata, "Periodically driven linear system with multiplicative colored noise," Phys. Rev. E, Vol. 57(6) , pp. 6555-6563, 1998; V. Berdichcvsky and M. Gitterman, "Stochastic resonance in linear systems subject to
multiplicative and additive noise", Phy. Rev. E, Vol. 60 (2) , pp. 1494-1499, 1999．
157． J.L. Cabrera, J. Gorronogoitia & F.J. Rubia, "Noise-correlation-time-mediated localization in random nonlinear dynamical systems," Phys. Rev. Lett, Vol. 82(14) , pp. 2816-2819, 1999．
158． Z. Hou & H. Xin, "Enhancement of stochastic resonance by noise delay," Phys. Lett. A, Vol. 263, pp. 360-364, 1999．
159． A. Giuliani, A. Colosimo, et ah, "On the constructive role of noise in spatial systems," Phys. Lett. A, Vol. 247, pp. 47-52, 1998．
160． C. Zhou & C.H. Lai, "Amplification of weak signals and stochastic resonance via on-off intermittency with symmetry breaking," Phys. Rev. E, Vol. 60(4) , pp. 3928-3935, 1999．
161． M.M. Alibegov, "stochastic resonance in threshold systems," Phys. Rev. E, Vol. 59(5) , pp. 4841-4846, 1999．
162． J.L. Ting, "Stochastic resonance for quantum channels," Phys. Rev. E, Vol. 59(3) , pp. 2801-2803, 1999．
163． J.M.G Vilar & J.M. Rubf, "Noise suppression by noise," Phys. Rev. Lett., Vol. 86(6) , pp. 950-953, 2001．
164． M. Rudolph & A. Destexhe, "Correlation detection and resonance in neural systems with distributed noise sources," Phys. Rev. Lett., Vol. 86(16) , pp. 3662-3665, 2001．
165． O.G. Calderon, "Stochastic resonance in free-electron lasers," Phys. Rev. E, Vol. 63(1) , p. 016502, 2000．
166． M. Piana, M. Canfora & M. Riani, "Role of noise in image processing by the human perceptive system," Phys. Rev. E, Vol. 62(1) , pp. 1104-1109, 2000．
167． J. Mason, J.F. Lindner, "Pulse-enhanced stochastic resonance," Phys. Lett. A, Vol. 277, pp. 13-17, 2000．
168． G Balazsi & L.B. Kish, "From stochastic resonance to brain waves," Phys. Lett. A, Vol. 265, pp. 304-316, 2000．
169． S.A. Guz, I.G Rusavin & M.V. Svirridov, "Broeain particle in a solitary potential well under the influence of 'green' noise," Phys. Lett. A, Vol. 274, pp. 104-110, 2000．
170． K. Loerincz, Z. Gingl, "Higher order stochastic resonance in a level-crossing detector," Phys. Lett. A, Vol. 254, pp. 154-157, 1999．
171． U.U. Muller & L.M. Ward, "Stochastic resonance in a statistical model of a time-integrating detector," Phys. Rev. E, Vol. 61(4) , pp. 4286-4294, 2000．
172． F. Chapeau-Blondeau, "Stochastic resonance at phase noise in signal transmission," Phys. Rev. E, Vol. 61(1) , pp. 940-943, 2000．
173． N. Dombey, P. Kennedy & A. Calogeracos, "Supercriticality and transmission resonance in the dirca equation," Phys. Rev. Lett., Vol. 85(9) , pp. 1787-1790, 2000．
174． S.F. Huelga& MB. Plenio, "Quantum stochastic resonance in electron shelving," Phys. Rev. A, Vol. 62(5) , p. 052111,2000．
175． M. Qian, G Wang & X. Zhang, "Stochastic resonance on a circle without excitation: Physcial investigation and peak frequency formula," Phys. Rev. E, Vol. 62(5) , pp. 6469-6474, 2000．
176． M. Litong, Y. Hayakawa & Y. Sawada, "Effect of noise coherence on stochastic resonance enhancement in a bithreshold system," Phys. Rev. E, Vol. 64(2) , p. 026117, 2001．
177． F.Moss & X. Pei, "Neurons in parallel," Nature, Vol. 376, pp. 211-212, 1995．
178． S.M. Bezrukov & I Vodyanoy, "Stochastic resonance in non-dynamical systems without response thresholds," Nature, Vol. 385, pp. 319-321, 1997．
179． G Qin, D. Gong, G Hu, et al. "An analog simulation of stochastic resonance," ACTA Phys. SINICA, Vol. 41(3) , pp. 360-369, 1992．
180． B.R. Pamas, "Noise and neuronal populations conspire to encode simple waveforms reliably," IEEE Trans. Biomed. Eng., Vol. 43(3) , pp. 313-318, 1996．
181． S. Sancho & A. Suarez, "Nonlinear dynamics of microwave synthesizers-stability and noise", IEEE Trans.
Micro. Theory & Tech., Vol. 49(10) , pp. 1792-1803, 2001．
182． B. Ando, S. Baglio, "Measurements of parameters influencing the optimal noise level in stochastic systems," IEEE Trans. Instrumentation & Measurement, Vol. 49(5) , pp. 1137-1142,2000．
183． N. Hohn & A.N. Burkitt, "Modelling the neural response to speech: stochastic resonance and coding vowel-like stimuli," IEEE EMBS Confer. Monash University, pp. 1-4, 2001．
184． F. Chapeau-Blondeau, "Nonlinear test statistic to improve signal detection in non-Gaussian noise," IEEE Sig, Proc. Lett., Vol. 7(7) , pp. 205-207, 2000．
185． H. Papadopoulos, G Wornell & A.V. ppenheim, "Low-complexity digital encoding strategies for wireless sensor networks," Pro. IEEE Int. Conf. On Acoustics, Speech, and Signal Processing, pp. 3273-3276, 1998．
186． H. Papadopoulos & G Wornell, "A class of stochastic resonance systems for signal processing applications," Pro. IEEE Int. Conf. On Acoustics, Speech, and Signal Processing, Atlanta, GA, 1996．
187． H.E. Plesser & T. Geisel, "Bandpass properties of integrate-fire neurons," Neurocomputing, 26-27, pp.229-235, 1999．
188． A. Restrepo, L.F. Zuluaga & L.E. Pino, "Optimal noise levels for stochastic resonance," IEEE Int. Conf. On Acoustic, Speech and Signal Processing, Vol. 3, pp. 2365-2368, 1997．
189． N. Hohn & A.N. Burkitt, "Enhanced stochastic resonance in threshold detectors," Neural Network, IEEE Int. Confer. IJCNN'01, Vol. 1, pp. 644-647, 2001．
190． D.W. Repperger, C.A. Phillips & A. Neidhard, "A study on stochastic resonance involving the Hodgkin-Huxley Equation," Proceeding of the American Control Confer., Arlington, pp.229-231, 2001．
191． M. Lim & C. Saloma, "Noise-enhanced measurement of weak doublet spectra with a Fourier-transform spectrometer and 1-bit analog-to-digital converter," Applied Optics, Vol. 40( 11) , pp. 1767-1775, 2001．
192． H.C. Papadopoulos, GW. Wornell & A.V. Oppenheim, "Sequential Signal Encoding from Noisy Measurements Using Quantizers with Dynamic Bias Control," IEEE Trans. Inform. Theory, Vol. 47(3) , pp. 978-1002,2001．
193． F. Moss, "Stochastic resonance: a signal+noise in a two state system," Frequency Control, 1991． , Proceedings of the 45th Annual Symposium on, pp.649-658,1991．
194． A.R. Bulsara, F. Moss, "Single neuron dynamics: noise-enhanced signal processing," Neural Networks, 1991． 1991 IEEE International Joint Conference on, Vol. 1, pp. 420-425,1991．
195． S. Mizutani, T. Sano, & K. Shimohara, "Resonance in chaotic neural networks driven by a weak sinusoid," Neural Networks Proceedings, 1998． IEEE World Congress on Computational Intelligence. The 1998 IEEE InternationalJoint Conference on, Vol. 3, pp. 2551-2556,1998．
196． S. Mizutani, T. Sano, T. Uchiyama, et al. "Numerical studies of resonance in a sinusoidally driven chaotic neuron model and its network," Neural Networks 1997, Int. Con. on, Vol. 2, pp. 663-668, 1997．
197． H.A. Braun, H. Wissing, K. Schafer, et al. "Oscillation and noise determine signal transduction in shark multimodal sensory cells," Nature, Vol. 367, pp. 270-273, 1994．
198． S.M. Bezrukov & I Vodyanoy, "Noise-induced enhancement of signal transduction across vohage-dependent ion channels," Nature, Vol. 378, pp. 362-364, 1995．
199． R.P Morse & GF. Meyer, "The practical use of noise to improve speech coding by analogue cochlear implants," Chaos Solitons & Fractals, Vol. 11, pp. 1885-1894, 2000．
200． R.P. Morse & P. Roper, "Enhanced coding in a cochlear-implant model using additive noise: Aperiod stochastic resonance with tuning," Phys. Rev. E, Vol. 61(5) , pp. 5683-5692, 2000．
201． A.J. Matsuoka, J.T. Rubinstein, "The effects of interpulse interval on stochastic properities of electrical stimulation: Models and Measurements," IEEE Trans. Biomedical Eng,, Vol. 48(4) , pp. 416-424, 2001．
202． J.T.Rubinstein, B.S. Wilson, "Pseudospontaneous activity: stochastic independence of auditory nerve fibers
with electrical stimulation," Hearing Research, Vol. 127, pp. 108-118, 1999．
203． K.R. Henry & E.R. Lewis, "Cochlear nerve acoustic envelope response detection is improved by the addition of random-phased tonal stimuli," Hearing Research, Vol. 155, pp. 91-102, 2001．
204． F.G Zeng, Q.J. Fu & R. Morse, "Human hearing enhanced by noise," Brain Res., Vol. 869, pp. 251-255, 2000．
205． l.M. Collins, R.L. Miller & D. Ferguson, "On the relationship between noise and speech recognition in cochlear implant subjects: A theoretical and psychophysical study," Journal of the Acoustical Society of America, v 96, n 5 pt 1, Nov, p. 2731, 1994．
206． E. Lanzara, R.N. Mantegna, "Experimental study of a nonlinear system in the presence of noise; The stochastic resonance," Am. J. Phys., Vol. 65(4) , pp. 341-349,1997．
207． M. Locher, M.E. Inchiosa, "Theory of controlling stochastic resonance," Phys. Rev. E, Vol. 62(1) , pp. 317-327,2000．
208． B. Ando, S. Graziani, "A new IR displacement system based on noise added theory," Instrumentation and Measurement Technology Conference, 2001． IMTC 2001． Proceedings of the 18th IEEE, Vol. 1, pp. 482-485, 2001; B. Ando, S. Graziani, "Adding noise to improve measurement," IEEE Instrumentation & Measurement Magazine, Vol. 4(1) , pp.24-31, 2001． ; G Giuffrida, S. Graziani, N. Pitrone, "Signal recovery by using a QDW based approach," Instrumentation and Measurement Technology Conference, 2000． IMTC 2000． Proceedings of the 17th IEEE, Vol. 3, pp. 1512-1517, 2000． ; S. Baglio, S. Graziani, N. Pitrone, "Measurements of parameters influencing the optimal noise level in stochastic systems," Instrumentation and Measurement, IEEE Transactions on, Vol. 49(5) , pp. 1137-1143, 2000; S. Baglio, S. Graziani, N. Pitrone, "A system for the implementation of noise added system driving," Instrumentation and Measurement Technology Conference, 1999． IMTC/99． Proceedings of the 16th IEEE, Vol. 2, pp. 1059-1062, 1999; S. Baglio, S. Graziani, N. Pitrone, "A probabilistic approach to the threshold error reduction theory in bistable measurement devices," Instrumentation and Measurement Technology Conference, 1998． IMTC/98． Conference Proceedings. IEEE, Vol. 2, pp. 1307-1312, 1998． ; S. Baglio, S. Graziani, N. Pitrone, "Threshold error reduction in linear measurement devices by adding noise signal," Instrumentation and Measurement Technology Conference, 1998． IMTC/98． Conference Proceedings. IEEE, Vol. 1, pp. 42-46, 1998． ; N. Pitrone & S. Graziani, "Hysteresis Shaping in Stochastic Driven Systems," IEEE Trans INSTRUMENTATION & MEASUREMENT, Vol. 50(5) , pp. 1264-1269, 2001．
209． J. Tapson, "Stochastic resonance in a mode locked acoustic interferometer," Ultrasonics, Vol. 36, pp. 415-419, 1998．
210． L. Gammaitoni, M. Martinelli, "Stochastic resonance in paramagnetic resonance systems," J. Stat. Phys., Vol. 70(1-2) , pp. 425-435, 1993．
211． D. Petracchi, "What is the role of stochastic resonance?" Chaos, Solitons & Fractrals, Vol. 11, pp. 1827-1834,2000．
212． K. Loerincz, Z. Gingl & .L.B. Kiss, "A stochastic resonator is able to greatly improve signal-to-noise ratio," Phys. Lett. A, Vol. 224, pp. 63-67, 1996．
213． F. Chapeau-Blondeau, "Nonlinear test statistic to improve signal detection in non-Gaussian noise", IEEE Sig. Proc. Lett., Vol. 7(7) , pp. 205-207, 2000．
214． VS. Anishchenko, M.A. SAFONOVA & L.O. Chua, "Stochastic resonance in Chua's circuit driven by amplitude or frequency modulated signals," Int. J. Bifurcation & Chaos, Vol. 4(2) , pp. 441-446, 1994．
215． M. Morillo & J.G6mez-Ordonez, "Amplification and distortion of a period rectangular driving signal by a noisy bistable system", Phys. Rev. E, Vol. 51(2) , pp. 999-1003, 1995．
216． Proakis, J.G "Digital communications," Third Ed. New York: McGraw-Hill, pp.233-406, 1995．
217． Proakis, J.G & Salehi, M. "Contemporary communication systems using MATLAB," PWS Publishing company, 1997．
218． Schwartz, M. "Information transmission, modulation, and noise," Third Ed., McGraw-Hill, Inc., pp.390-570, 1980．
219． H. Risken, The Fokker-Planck Equation, Springer, New York, 1983．
220． B. Xu, F. Duan, R. Bao, et al. "Stochastic resonance with tuning system parameters: the application of bistable systems in signal processing," Chaos, Solitons & Fractals, Vol. 13(4) , pp. 633-644, 2002．
221． F. Duan & B. Xu, "Parameter-induced stochastic resonance and baseband binary PAM signal transmission over an AGWN channel," Int. J. Bifurcation & Chaos, Vol. 13(2) , 2003．
222． B. Xu, J. Li, F. Duan, et al. "Effects of colored noise on multi-frequency signal processing via stochastic resonance with tuning system parameters," Chaos, Solitons & Fractals, Vol. 16(1) , pp. 93-106,2003．
223． F. Duan, B. Xu, F. Chapeau-Blondeau, "Comparison of Stochastic Resonance via Adding Noise and That via Tuning System Parameters in Signal Transmission", Submitted to Phy. Rev. E.
224． J. Li, R. Bao, B. Xu, "Effects of some sort of nonlinear systems on signal processing via stochastic resonance with tuning system parameters," Accepted by Phys. A.
225． 段法兵，“参数调节随机共振在数字信号传输中的应用”，浙江大学博士论文。
2． R. Benzi, G. Parisi, & A. Vulpiani. "Stochastic resonance in climatic change," Tellus, Vol. 34, pp. 10-16, 1982．
3． L. Gammaitoni, P. Hanggi, P. Jung, et al. "Stochastic resonance," Rev. Mod. Phys., Vol. 70(1) , pp. 223-285, 1998．
4． S. Mitaim & B. Kosko, "Adaptive stochastic resonance," Pro. IEEE, Vol. 86(11) , pp. 2152-2183,1998．
5． S. Fauve & F. Heslot, "Stochastic resonance in a bistable system," Phys. Lett., Vol. 97A (1-2) , pp. 5-7, 1983．
6． B. McNamara, K. Wiesenfeld, & R. Roy, "Observation of stochastic resonance in a ring laser," Phys. Rev. Lett., Vol. 60, p. 2626,1988; "Theory of stochastic resonace," Phys. Rev. A, Vol. 39(9) , pp. 4854-4868, 1989．
7． K. Wiesenfeld & F. Jaramillo, "Minireview of stochastic resonance," Chaos, Vol. 8(3) , pp. 539-548, 1998．
8． K. Wiesenfeld & F. Moss, "Stochastic resonance and the benefits of noise: from ice ages to crayfish and SQUIDs," Nat., Vol. 373, pp. 33-36, 1995．
9． F. Moss, D. Pierson & D. O'Gorman, "Stochastic resonance: Tutorial and update," Int. J. Bifur. & Chaos, Vol. 4(6) , pp. 1383-1397,1994．
10． A.R. Bulsara & L. Gammaitoni, "Tuning in to noise," Phys. Today, Vol. 49(3) , pp. 39-45,1996．
11． M.I. Dykman, "What can stochastic resonance do?" Nature, Vol. 391, p. 344, 1998．
12． D.G Luchinsky, R. Mannella, P.V.E. McClintock, et al. "Stochastic resonance in electrical circuits-Ⅰ: Conventional stochastic resonance," IEEE Trans. Cir. & Sys.-Analog and digital signal processing, Vol. 40(9) , pp. 1205-1214,1999．
13． D.G Luchinsky, R. Mannella, P.V.E. McClintock, et al. "Stochastic resonance in electrical circuits-Ⅱ: Nonconventional stochastic resonance," IEEE Trans. Cir. & Sys.-Analog and digital signal processing, Vol. 40(9) , pp. 1215-1224,1999．
14． B. McNamara & K. Wiesenfeld, "Theory of stochastic resonance," Phys. Rev. A., Vol. 39(9) , pp. 4854-4869, 1989．
15． L. Gammaitoni, F. Marchesoni, E. Menichella-Saetta et al. "Stochastic resonance in bistable systems," Phys. Rev. Lett., Vol. 62(4) , p. 349, 1989．
16． M.I. Dykman, R. Mannella, P.V.E. McClintock, et al. "Comment on 'Stochastic resonance in bistable systems'," preceding Comment, Phys. Rev. Lett., Vol. 65, p. 2606, 1990．
17． M.I. Dykman, D.G Luchinsky, et al., "Stochastic resonance: Linear response theory and giant nonlinearity," J. Stat. Phys., Vol.70 (1/2) , pp. 463-479,1993．
18． M.I. Dykman, R. Mannella, P.V.E. McClintock, et al, "Giant nonlinearity in the low-frequency response of a fluctuating bistable system," Phys. Rev. E, Vol. 47(3) , pp. 1629-1632, 1993． "Spectral density fluctuations of a double-well Duffing oscillator driven by white noise," Phys. Rev. A, Vol. 37(4) , pp. 1303-1312, 1988．
19． T. Zhou & F. Moss, "Analog simulations of stochastic resonance," Phys. Rev. A, Vol. 41(8) , pp. 4255-4264, 1990．
20． M.H. Choi, R.F. Fox & P. Jung, "Quantifying stochastic resonance in bistable systems: response vs residence-time distribution functions," Phys. Rev. E, Vol. 57(6) , pp. 6335-6344, 1998．
21． L. Gammaitoni, F. Marchesoni, & S. Santucci, "Stochastic Resonance as a Bona Fide resonance", Phys. Rev. Lett., Vol. 74, p. 1052, 1995．
22． G Giacomelli, F. Maria & I. Rabbiosi, "Stochastic and bona-fide resonance: an experimental investigation," Phys. Rev. Lett., Vol. 82(4) , pp. 675-678, 1999．
23． P. Hanggi & P.V.E. McClintock, "Bistablity driven by colored noise: Theory and experiment," Phys. Rev. A, Vol. 32(1) , pp. 695-698,1985．
24． P. Jung & P. Hanggi, "Stochastic nonlinear dynamic modulated by external periodic forces," Europhys. Lett., Vol. 8(6) , pp. 505-510, 1989．
25． R. F. Fox, "Stochastic resonance in a double well," Phys. Rev. A, Vol. 39(8) , pp. 4148-4153,1989．
26． P. Jung & P. Hanggi, "Amplification of small signals via stochastic resonance," Phys. Rev. A, Vol. 44(12) , pp. 8032-8042, 1991．
27． Hu G, G Nicolis & C. Nicolis, "Periodically forced Fokker-Planck equation and stochastic resonance," Phys. Rev. A, Vol. 42(4) , pp. 2030-2041, 1990．
28． JJ. Collins, C.C. Chow, & T.T. Imhoff, "Aperiod stochastic resonance in excitable systems," Phys. Rev. E, Vol. 52(4) , pp. R3321-3324, 1995．
29． J.J. Collins, C.C. Chow, A.C. Capela, et al. "Aperiod stochastic resonance," Phys. Rev. E, Vol. 54(5) , pp. 5575-5584, 1996．
30． C. Heneghan, C.C. Chow, J.J.Collins, et al. "Information measures quantifying aperiod stochastic resonance," Phys. Rev. E, Vol. 54(3) , R2228-2231,1996．
31． J.J. Collins, T.T. Imhoff, & P. Grigg, "Noise-enhanced tactile sensation," Nature, Vol. 383, p. 770, 1996．
32． A.R. Bulsara & A. Zador, "Threshold detection of wideband signal: A noise-induced maximum in the mutual information," Phys. Raw. E, Vol. 54(3) , pp. R2185-2188, 1996．
33． A. Neiman, B. Shulgin, V. Anishchenko, et al. "Dynamical entropies applied to stochastic resonance," Phys. Rev. Lett, Vol. 76(23) , pp. 4299-4302, 1996．
34． Hu G, Gong D., Wen X., et al., "Stochastic resonance in a nonlinear system driven by an apeoridic force," Phys. Rev. A, Vol. 46(6) , pp. 3250-3254,1992．
35． M. Stemmler, "A single spike suffices: the simplest form of stochastic resonance in model neurons," Network: Comput. Neural Sys, Vol. 7, pp. 687-716, 1996．
36． L. Glass, "Synchronization and rhythmic processes in physiology," Nature, Vol. 410, pp. 277-284, 2001．
37． F. Chapeau-Blondeau. "Noise-enhanced capacity via stochastic resonance in an asymmetric binary channel," Phys. Rev. E, Vol. 55(2) , pp. 2016-2019, 1997．
38． X. Godivier, J. Rojas-Varela, & F. Chapeau-Blondeau, "Noise-assisted signal transmission via stochastic resonance in a diode non-linearity," Electronics Letters, Vol. 33(20) , pp. 1666-1668, 1997．
39． X. Godivier & F. Chapeau-Blondeau, "Noise-assisted signal transmission in a nonlinear electronic comparator: Experiment and theory," Signal Processing, Vol. 56, pp. 293-303, 1997．
40． F. Chapeau-Blondeau & X. Godivier, "Theory of stochastic resonance in signal transmission by static nonlinear systems," Phys. Rev. E, Vol. 55(2) , pp. 1478-1495, 1997．
41． J.W.C. Robinson & D.E. Asraf, "Information-theoretic distance measures and a generalization of stochastic resonance," Phys. Rev. E, Vol. 81(14) , pp. 2850-2853,1998．
42． X. Godivier & F. Chapeau-Blondeau, "Stochastic resonance in the information capacity of a nonlinear dynamic systems," Phys. Rev. E, Vol. 8(3) , pp. 581-589, 1998．
43． M.E. Inchiosa & A.R. Bulsara, "dc signal detection via dynamical asymmetry in a nonlinear device," Phys. Rev. E, Vol. 58(1) , pp. 115-127, 1998．
44． F. Chapeau-Blondeau, "Stochastic resonance and optimal detection of pulse trains by threshold devices," Dig. Sig. Proc., Vol. 9, pp. 162-177,1999．
45． S. Zozor & P.O. Amblard, "Stochastic resonance in discrete time nonlinear AR(1) Models," IEEE Trans, on Sig. Proc., Vol. 47(1) , pp. 108-121, 1999．
46． F. Chapeau-Blondeau, "Periodic and aperiodic stochastic resonance with output signal-to-noise ratio
exceeding that at the input," Int. J. Bifurcation and Chaos, Vol. 9(1) , pp. 267-272,1999．
47． D.F Russell, L.A. Wilkens, & Frank Moss, "Use of behavioral stochastic resonance by paddle fish for feeding," Nature, Vol. 402, pp. 291-293,1999．
48． J.E. levin & J.P. Miller, "Broadband neural encoding in the cricket cereal sensory system enhanced by stochastic resonance," Nature, Vol. 380(14) , pp. 165-168, 1996．
49． S. Barbay, G Giacomelli & F. Marin, "Experimental evidence of binary aperiod stochastic resonance," Phys. Rev, Lett., Vol. 85(22) , pp. 4652-4655, 2000．
50． I. Goychuk & P. Hanggi, "Stochastic resonance in ion channels characterized by information theory," Phys. Rev. E, Vol. 61(4) , pp. 4272-4280,2000．
51． M.N. Lorenzo, V. Perez-Mufluzuri & V. Perez-Villar, "Noise performance of a synchronization scheme through compound chaotic signal," Int. J. Bifurcation & Chaos, Vol. 10(12) , pp. 2863-2870, 2000．
52． R.P. Morse & P. Roper, "Enhanced coding in a cohlear-implant model using additive noise: Aperiod stochastic resonance with tuning," Phys. Rev. E, Vol. 61(5) , pp. 5683-5692,2000．
53． EL Naschie MS, Gebeshuber IC, A.V. Holden & D. Petracchi, eds. "Stochastic resonance in biological systems," Chaos, Solitons & Fractals, Vol. 11, 2000．
54． T. Wellens & A. Buchleither, "Bistability and stochastic resonance in an open quantum system," Phys. Lett. A, Vol. 268, pp. 131-149,2001．
55． H.E. Plesser & T. Geisel, "Signal processing by means of noise," NEUROCOMPUTING, Vol. 38, pp. 307-312,2001．
56． M. Rudolph & A. Destexhe, "Correlation detection and resonance in neural systems with distributed noise sources," Phys. Rev. Lett., Vol. 86(16) , pp. 3662-3665,2001．
57． F. Liu & W. Wang, "Frequency sensitivity in nervous systems," Chi. Phys. Lett., Vol. 18(2) , pp. 292-294, 2001．
58． V. Schulter-Frohlinde, Y. Ashkenazy & P. Ch. Ivanov, "Noise effects on the complex patterns of abnormal heartbeats," Phys. Rev. E, Vol. 87(6) , p. 068104,2001．
59． N.G Stocks & R. Mannella, "Generic noise-enhanced coding in neuronal arrays," Phys. Rev. E, Vol. 64(3) , p. 030902, 2001
60． T. Kanamaru & T. Horita, "Theoretical analysis of array-enhanced stochastic resonance in ddiffusively coupled FitzHugh-Nagumo equation," Phys. Rev. E, Vol. 64(3) , p. 031908,2001．
61． L. Schimansky-Geier, J.A. Freund, "Noise induced order: stochastic ewsonance," Int. J. Bifurcation & Chaos, Vol. 8(5) , pp. 869-879,1998．
62． N.G Stocks, "Suprathreshold stochastic resonance in multilevel threshold systems," Phys. Rev. Lett., Vol. 84(11) , pp. 2310-2313,2000．
63． N.G Stocks, "Suprathreshold stochastic resonance: an exact result for uniformly distributed signal and noise," Phys. Lett. A, Vol. 279, pp. 308-312, 2001．
64． JJ. Collins, C.C. Chow & T.T. Imhoff, "Stochastic resonance without tuning," Nat., Vol. 376, pp. 236-239, 1995．
65． J.E. Fletcher, S. Havlin & GH. Weiss, J.Stat. Phys. Vol. 51, p. 215, 1988．
66． J. Masoliver & A. Robinson, "Coherent stochastic resonance," Phys. Rev. E, Vol. 51(5) , pp. 4021-4026, 1995．
67． J.M. Porra, "When coherent stochastic resonance appears," Phys. Rev. E, 55(6) , pp.6533-6539, 1997．
68． A.K. Dhara & T. Mukhopadhyay, "Coherent stochastic resonance in the case of two absorbing boundaries," Phys. Rev. E, Vol. 60(3) , pp. 2727-2736, 1999．
69． P.O. Amblard & S. Zozor, "Cyclostationary and stochastic resonance in threshold devices," Phys. Rev. E, Vol. 59(5) , pp. 5009-5020,1999．
70． S. Mitaim, B. Kosko, "Neural fuzzy stochastic resonance," Systems, Man, and Cybernetics, IEEE International Conference on , Vol. 3 , pp. 2237-2242, 1998．
71． S. Mitaim, B. Kosko, "Adaptive stochastic resonance with fuzzy systems," Fuzzy Information Processing Society-NAFIPS, Conference of the North American, pp. 355-359, 1998．
72． S. Mitaim, B. Kosko, "Adaptive stochastic resonance and fuzzy approximation," Intelligent Control (ISIC), Intelligent Systems and Semiotics (ISAS), Proceedings of the 1998 IEEE International Symposium on, pp. 471-476, 1998．
73． P.Jung, U.Behn, E. Pantazelou & F. Moss, Phys. Rev. A, Vol. 46, p.R 1709, 1992．
74． J.F. Lindner, B.K. Meadows & W.L. Ditto, "Array enhanced stochastic resonance and spatiotemporal synchronization," Phys. Rev. Lett., Vol. 75(1) , pp. 3-6,1995．
75． M.E. Inchiosa & A.R. Bulsara, "Signal detection statistics of stochastic resonators," Phys. Rev. E, Vol. 53(3) , pp. R2021-2024, 1996．
76． T.R. Albert, A.R. Bulsara, G Schmera, et al. "An evaluation of the stochastic resonance phenomenon as a potential tool for signal processing," Signals, Systems and Computers, 1993, Conference Record of The Twenty-Seventh Asilomar Conference on.. Vol. 1, pp. 583-587, 1993
77． Neff, J.D.; Patel, GN.; Meadows, B.K.; DeWeerth, S.P.; Ditto, W.L. "Spatiotemporal dynamics of a stochastic VLSI array," Circuits and Systems, ISCAS '98． Proceedings of the 1998 IEEE International Symposium on, Vol. 3, pp: 542-545．
78． P. Arena, R. Caponetto, L. Fortuna, et al. "Noise-supported wavefronts in cellular neural networks," IEEE Trans. Cir. & Sys.-I: Fundmental theory and Application, Vol. 43(3) , pp. 360-363, 2001．
79． D.E. Postnov & O.V. Sosnovtseva, "Stochastic synchronization of coupled coherence resonance oscillators," Int. J. Bifurcation & Chaos, Vol. 10(11) , pp. 2541-2550, 2000．
80． Zhang Y., Hu G & L. Gammaitoni, "Signal transmission in one-way coupled bistable system: noise effect," Phys. Rev. E, Vol. 58(3) , pp. 2952-56,1998．
81． F. Chapeau-Blondeau & J. Rojas-Varela, "Nonlinear signal propagation enhanced by noise via stochastic resonance," Int. J. Bifurcation & Chaos, Vol. 10(8) , pp. 1951-1959,2000．
82． V. I. Sbitney & M.A. Pustovoit, "Stochastic resonance in 2D coupled map lattice model of field-like neural tissue," Int. J. Bifurcation & Chaos, Vol. 10(8) , pp. 1961-1971, 2000．
83． U. Siewert & L. Schimansky-Geier, "Analytical study of coupled two-state stochastic resonance," Phys. Rev. E, Vol. 58(3) , pp. 2843-2852, 1998．
84． Zhou C., J. Kurths & B. Hu, "Array-enhanced coherence resonance: nontrivial effects of heterogeneity and spatial independence of noise," Phys. Rev. Lett., Vol. 87(9) , p. 098101, 2001．
85． A.A. Zaikin, K. Murali & J. Kurths, "Simple electronic circuit model for doubly stochastic resonance," Phys. Rev. E, Vol. 63(2) , p. 020103, 2001．
86． T. Kanamaru, T. Horita & Y. Okabe, "Theoretical analysis of array-enhanced stochastic resonance in the diffusively coupled FitzHugh-Nagumo equation," Phys. Rev. E, Vol. 64(3) , p. 031908, 2001．
87． N.G Stocks & P. Mannella, "Generic noise-enhanced coding in neural arrays," Phys. Rev. E, Vol. 64(3) , p. 030902,2001．
88． Y. Horikawa, "Coherence resonance with multiple peaks in a coupled FitzHugh-Nagumo model," Phys. Rev. ?Vol. 64(3) , p. 031905,2001．
89． C. Hauptmann, F. Kaiser & C. Eichwals, "Signal transfer and stochastic resonance in copied nonlinear systems," Int. J. Bifurcation & Chaos, Vol. 9(6) , pp. 1159-1167, 2000．
90． G Mato, "Stochastic resonance using noise generated by a neural network," Phys. Rev. E, Vol. 59(3) , pp. 3339-43, 1999．
91． S. Kim, S.H. Park & H.B. Pyo, "Stochastic resonance in coupled oscillator systems with time delay," Phys. Rev. Lett., Vol. 82(8) , pp. 1620-23, 1999．
92． A. Krawiecki, A. Sukiennicki & R.A. Kosinski, "Stochastic resonance and noise-enhanced with spatitemporal periodic signal," Phys. Rev. E, Vol. 62(6) , pp. 7683-89,2000．
93． A.A. Zaikin, J.Kurths & L. Schimansky-Geier, "Doubly stochastic resonance," Phys. Rev. Lett., Vol. 85(2) , pp. 227-231,2000．
94． N. Sungar, J.P. Sharpe & S. Weber, "Stochastic resonance in two-dimensional arrays of copied nonlinear oscillators," Phys. Rev. E, Vol. 62(1) , pp. 1413-15,2000．
95． B. Lindner & L. Schimansky-Geier, "Transmission of noise coded versus additive signal through a neuronal ensemble," Phys. Rev. Lett., Vol. 86(4) , pp. 2934-2937, 2001．
96． T. Kapitaniak, "Stochastic resonance in Chaotically forced systems," Chaos, Solitons & Fractals, Vol. 3(4) , pp. 405-410, 1993．
97． VS. Anishchenko, M.A. Safonova & L.O. Chua, "Stochastic resonance in Chua's circuit," Int. J. Bifurcation & Chaos, Vol. 2(2) , pp. 397-401, 1992． "Stochastic resonance in the nonautonomous Chua's circuit," J. Cir., Sys. & Comp., Vol. 3(2) , pp. 553-578, 1993．
98． O. Calvo, C.R. Mirasso & R. Toral, "Coherence resonance in chaotic electronic circuits," Electronics Lett., Vol. 37(17) , pp. 1062-63,2001．
99． Hu G, L. Pivka& A.L. Zheleznyak, "synchronization of a one-dimensional array of Chua's circuits by feedback control and noise," IEEE Trans. Cir & Sys.-I: Fundamental theory and Application, Vol. 42(10) , pp. 736-40,1995．
100． S. Mizutani, T. Sano & T. Uchiyama, "Numerical studies of resonance in a sinusoidally driven chaotic neuron model and its network," Neural Network, Int. Confer. On, Vol. 2, pp. 663-8, 1997．
101． J.Y. Ko, K. Otsuka & T. Kubota, "Quantum-noise-induced order in lasers placed in chaotic oscillation by frequency-shifted feedback," Phys. Rev. Lett., Vol. 86(18) , pp. 4025-28,2001．
102． S.Matyjaskiewicz, A. Krawiecki, et al., "Stochastic multiresonance in a chaotic map with fractal basins of attraction," Phys. Rev. E, Vol. 63(2) , p. 026215, 2001．
103． GD. VanWiggeren & R. Roy, "Communication with chaotic lasers," Science, Vol. 279, pp. 1198-1200, 1998．
104． V.N. Chizhevsky, R. Vilaseca & R. Corbalan, "Amplification of near-resonant signals via stochastic resonance in a chaotic CO2 laser," Phys. Rev. Lett., Vol. 61(6) , pp. 6500-6505,2000．
105． R.M. Siegel & H.L. Read, "Models of the temporal dynamics of visual processing," J. Stat. Phys., Vol. 70(1/2) , pp. 297-308, 1993．
106． D.R. Chialvo & A.V. Apkarian, "Modulated noisy biological dynamics: three examples,' J. Stat. Phys., Vol. 70(1/2) , pp. 375-390, 1993．
107． M. Misono, T. ohmoto, "Noise-enhanced transmission of information in a bistable system," Phys. Rev. E, Vol. 58(5) , pp. 5602-5607, 1998．
108． M. Riani & E. Simonotto, "Stochastic resonance in the perceptual interpretation of ambiguous figures: A neural network model," Phys. Rev. Lett., Vol. 72(19) , pp. 3120-23,1994．
109． M. Stemmler, M. Usher & E. Niebur, "Interaction in primary visual cortex: A model bridging physiology and psychophysics," Science, Vol. 269, pp. 1877-1880, 1995．
110． T. Yang, "Adaptively optimizing stochastic resonance in visual system," Phys. Lett. A, Vol. 245, pp. 79-86, 1998．
111． J.S. Anderson, I. Lampl, et al., "The contribution of noise to contrast invariance of orientation tuning in cat visual cortex," Science, Vol. 290, pp. 1968-72, 2000．
112． GP. Harmer & D. Abbott, "Motion detection and stochastic resonance in noisy environments,"
Microelectronics J., Vol. 32, pp. 959-967, 2001．
113． T. Ditzinger, M. Stadler, et al., "Noise improve three-dimensional perception: Stochastic resonance and other impacts of noise to the perception of autostereograms," Phys. Rev. E, Vol. 62(2) , pp. 2566-2575, 2000．
114． M. Nafie & A.H.Tewfik, "Low power detection using stochastic resonance," The Thirty-Second Asilomar. Conf. On Signal, System and Computer, 1998．
115． A.S. Asdi & A.H. Tewfik, "Detection of weak signals using adaptive stochastic resonance," Pro. IEEE Int. Conf. OnAcoustics, Speech, and Signal Processing, Detroit, MI, 1995．
116． F. Vaudelle, J. Gazengel, et al., "Stochastic resonance and noise-enhanced transmission of spatial signals in optics: the case of scattering." J. Opt. Soc. Am. B, Vol. 15(11) , pp. 2674-2680, 1998．
117． E. Simonotto, M. Riani, et al., "Visual perception of stochastic resonance," Phys. Rev. Lett., Vol. 78(6) , pp. 1186-1189, 1997．
118． L. Gammaitoni, "Stochastic resonance in multi-threshold systems," Phys. Lett. A, Vol. 208, pp. 313-32, 1995．
119． L. Gammaitoni, "Stochastic resonance and dithering effect in threshold physical systems," Phys. Rev. E, Vol. 52(5) , pp. 4691-4698, 1995．
120． R.A. Wannamaker, S.P. Lipshitz & J. Vanderkoov, "Stochastic resonance as dithering," Phys. Rev. E, Vol. 61(10) , pp. 233-236, 2000．
121． R.A. Wannamaker, S.P. Lipshitz, J. Vanderkoov & J.N. Wright, "A theory of nonsubtractive dither," IEEE Trans. Sig. Proc., Vol. 48(2) , pp. 499-516, 2000．
122． J.F. Blinn, "Quantization error and dithering," IEEE Computer. Graphics & Application, pp. 78-82． July, 1994．
123． Hu G, T. Ditzinger, et al., "Stochastic resonance without external periodic force," Phys. Rev. Lett., Vol. 71(6) , pp. 807-810, 1993．
124． A.S. Pikovsky & J. Kurths, "Coherence resonance in noise-driven excitable system," Phys. Rev. Lett., Vol. 78(5) , pp. 775-778, 1997．
125． S.G Lee, A. Neiman & S. Kim, "Coherence resonance in a Hodgkin-Huxley neuron," Phys. Rev. E, Vol. 57(3) , pp. 3292-3297, 1998．
126． P. Jung, "Stochastic resonance and optimal design of threshold detectors," Phys. Lett. A, Vol. 220, pp. 219-223, 1995．
127． J.M.G Vilar, A. Perez-Madrid and J.M. Rubi, "Stochastic resonance in a dipole", Phy. Rev. E, Vol. 54(6) , pp. 6929-6932, 1997．
128． J.M.G Vilar and J.M. Rubi, "Stochastic Multiresonance", Phy. Rev. Lett., Vol. 78(15) , pp. 2882-2885, 1997．
129． N.G Stocks, N.D. Stein & P.V.E. McClintock, J. Phys. A: Math. Gen., Vol. 25, pp. L1119, 1992． "Stochastic resonance in monostable systems," J. Phys. A: Math. Gen., Vol. 26, pp. L385-390, 1993．
130． J.M.G Vilar & J.M. Rubf, "Divergent signal-noise ratio and stochastic resonance in monostable systems," Phys. Rev. Lett., Vol. 77(4) , pp. 2863-66, 1996．
131． A.N. Grigorenko, S.I. Nikitin & GV. Roschepkin, "Stochastic resonance at higher harmonics in monostable systems," Phys. Rev. E, Vol. 56(5) , pp. R4907-4910, 1997．
132． L. Alfonsi, L. Gammaitoni, S. Santucci, et al. "Intrawell stochastic resonance versus inter-well stochastic resonance," Phys. Rev. E, Vol. 62(1) , pp. 299-302, 2000．
133． K. Wiesenfeld, D. Pierson, "Stochastic resonance on a circle," Phys. Rev. Lett., Vol. 72(14) , pp. 2125-2129, 1994．
134． I.K. Kaufman, D.G Luchinsky, "High-frequency stochastic resonance in SQUIDs," Phys. Lett. A, pp. 219-223, Sep. 1996．
135． F. Moss, A. Bulsara, and M.F. Shlesinger, J. Stat. Phys. Vol. 70(1-2) , 1993; Bulsara A., Moss F., Phys. Rev.
Lett., Vol. 67, pp. 656-659, 1991．
136． J.K. Douglass, L. Wilkens, E. Pantazelou, et al. "Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance," Nature, Vol. 365, pp. 337-340, 1993．
137． D. Nozaki & Y. Yamamoto, "Enhancement of stochastic resonance in a FitzHugh-Nagumo neuronal model driven by colored noise," Phys. Lett., A, Vol. 243, pp. 281-287, 1998．
138． T. Shimokawa, A. Rogel, "Stochastic resonance and spike-timing precision in an ensemble of leaky integrate and fire neuron models," Phys. Rev. E, Vol. 59(3) , pp. 3461-3470,1999．
139． T. Ohira & Y. Sato, "Resonance and delay," Phys. Rev. Lett., Vol. 82(14) , pp. 2811-2815, 1999．
140． V. Galdi, V. Pierro & I.M. Pinto, "Evaluation of stochastic-resonance-based detectors of weak harmonic signals in additive white Gaussian noise," Phys. Rev. E, Vol. 57(6) , pp. 6470-6479,1998．
141． M.C. Eguia, M.I. Rabinovich & H.D. Abarbanel, "Information transmission and recovery in neural communication channels," Phys. Rev. E, Vol. 62(5) , pp. 7111-7122, 2000．
142． V.A. Shneidman, P. Jung & P Hanggi, "Weak-noise limit of stochastic resonance," Phys. Rev. Lett., Vol. 72(17) , pp. 2682-2685,1994．
143． R. Lofstedt & S.N. Coppersmith, "Stochastic resonance: Nonperturbative calculation of power spectra and residence-time distribution," Phys. Rev. E, Vol. 49(6) , pp. 4821-4831, 1994．
144． S. Matyjaskiewicz, A. Krawiecki, "Stochastic multiresonance in a chaotic map with fractal basins of attraction," Phys. Rev. E, Vol. 63(2) , p. 026215, 2001．
145． J.A. Gonzalez, I.I. Reyes & L.E. Guerreo, "Solutions to chaotic and stochastic resonance," Chaos, Vol. 11(1) , pp. 1-15,2001．
146． D.T.W. Chik, Y. Wang & Z.D. Wang, "Stochastic resonance in a Hodgkin-Huley neuron in the absence of external noise," Phys. Rev. E, Vol. 64(2) , p. 021913, 2001．
147． I. Goychuk, "Information transfer with rate-modulated Poisson processes: A simple model for nonstationary stochastic resonance," Phys. Rev. E, Vol. 64(2) , p. 021909, 2001．
148． H.E. Plesser & T. Geisel, "Stochastic resonance in neuron models: Endogenous stimulation revisited,'" Phys. Rev. E, Vol. 63(3) , p. 031916, 2001．
149． MR Carusela, R.P.J. Perazzo & L. Romanelli, "Stochastic resonance memory storage device," Phys. Rev. E, Vol. 64(3) , p. 031101,2001．
150． GP. Harmer & D. Abbott, "Simulation of circuits demonstrating stochastic resonance," Microelectronics J., Vol. 31, pp. 553-559,2000．
151． K. Lerincz, Z. Gingl & L.B. Kiss, "A stochastic resonator is able to greatly improve signal-to-noise," Phys. Lett. A, Vol. 224, pp. 63-67, 1996．
152． F. Chapeau-Blondeau, "Input-output gains for signal in noise in stochastic resonance," Phys. Lett. A, Vol. 232, pp. 41-48, 1997．
153． M.T. Blackwell, "Effect of white and filtered noise on contrast detection thresholds," Vision Res., Vol. 38(2) , pp. 267-280,1998．
154． F. Marchesoni, F. Apostolico, "Color effects in a near-threshold Schmitt trigger," Phys. Rev. E, Vol. 58(6) , pp. 7079-84,1998．
155． J.M.G Vilar & R.V. Sole, "Effects of noise in symmetric two-species competition," Phys. Rev. Lett., Vol. 80(18) , pp. 4099-4102, 1998．
156． A. Fulinski, "Relaxation, noise-induced transitions, and stochastic resonance driven by non-Markovian dichotomic noise", Phy. Rev. E, Vol. 52(4) , pp. 4523-4526, 1995; A.V. Barzykin, K. Seki & F. Shibata, "Periodically driven linear system with multiplicative colored noise," Phys. Rev. E, Vol. 57(6) , pp. 6555-6563, 1998; V. Berdichcvsky and M. Gitterman, "Stochastic resonance in linear systems subject to
multiplicative and additive noise", Phy. Rev. E, Vol. 60 (2) , pp. 1494-1499, 1999．
157． J.L. Cabrera, J. Gorronogoitia & F.J. Rubia, "Noise-correlation-time-mediated localization in random nonlinear dynamical systems," Phys. Rev. Lett, Vol. 82(14) , pp. 2816-2819, 1999．
158． Z. Hou & H. Xin, "Enhancement of stochastic resonance by noise delay," Phys. Lett. A, Vol. 263, pp. 360-364, 1999．
159． A. Giuliani, A. Colosimo, et ah, "On the constructive role of noise in spatial systems," Phys. Lett. A, Vol. 247, pp. 47-52, 1998．
160． C. Zhou & C.H. Lai, "Amplification of weak signals and stochastic resonance via on-off intermittency with symmetry breaking," Phys. Rev. E, Vol. 60(4) , pp. 3928-3935, 1999．
161． M.M. Alibegov, "stochastic resonance in threshold systems," Phys. Rev. E, Vol. 59(5) , pp. 4841-4846, 1999．
162． J.L. Ting, "Stochastic resonance for quantum channels," Phys. Rev. E, Vol. 59(3) , pp. 2801-2803, 1999．
163． J.M.G Vilar & J.M. Rubf, "Noise suppression by noise," Phys. Rev. Lett., Vol. 86(6) , pp. 950-953, 2001．
164． M. Rudolph & A. Destexhe, "Correlation detection and resonance in neural systems with distributed noise sources," Phys. Rev. Lett., Vol. 86(16) , pp. 3662-3665, 2001．
165． O.G. Calderon, "Stochastic resonance in free-electron lasers," Phys. Rev. E, Vol. 63(1) , p. 016502, 2000．
166． M. Piana, M. Canfora & M. Riani, "Role of noise in image processing by the human perceptive system," Phys. Rev. E, Vol. 62(1) , pp. 1104-1109, 2000．
167． J. Mason, J.F. Lindner, "Pulse-enhanced stochastic resonance," Phys. Lett. A, Vol. 277, pp. 13-17, 2000．
168． G Balazsi & L.B. Kish, "From stochastic resonance to brain waves," Phys. Lett. A, Vol. 265, pp. 304-316, 2000．
169． S.A. Guz, I.G Rusavin & M.V. Svirridov, "Broeain particle in a solitary potential well under the influence of 'green' noise," Phys. Lett. A, Vol. 274, pp. 104-110, 2000．
170． K. Loerincz, Z. Gingl, "Higher order stochastic resonance in a level-crossing detector," Phys. Lett. A, Vol. 254, pp. 154-157, 1999．
171． U.U. Muller & L.M. Ward, "Stochastic resonance in a statistical model of a time-integrating detector," Phys. Rev. E, Vol. 61(4) , pp. 4286-4294, 2000．
172． F. Chapeau-Blondeau, "Stochastic resonance at phase noise in signal transmission," Phys. Rev. E, Vol. 61(1) , pp. 940-943, 2000．
173． N. Dombey, P. Kennedy & A. Calogeracos, "Supercriticality and transmission resonance in the dirca equation," Phys. Rev. Lett., Vol. 85(9) , pp. 1787-1790, 2000．
174． S.F. Huelga& MB. Plenio, "Quantum stochastic resonance in electron shelving," Phys. Rev. A, Vol. 62(5) , p. 052111,2000．
175． M. Qian, G Wang & X. Zhang, "Stochastic resonance on a circle without excitation: Physcial investigation and peak frequency formula," Phys. Rev. E, Vol. 62(5) , pp. 6469-6474, 2000．
176． M. Litong, Y. Hayakawa & Y. Sawada, "Effect of noise coherence on stochastic resonance enhancement in a bithreshold system," Phys. Rev. E, Vol. 64(2) , p. 026117, 2001．
177． F.Moss & X. Pei, "Neurons in parallel," Nature, Vol. 376, pp. 211-212, 1995．
178． S.M. Bezrukov & I Vodyanoy, "Stochastic resonance in non-dynamical systems without response thresholds," Nature, Vol. 385, pp. 319-321, 1997．
179． G Qin, D. Gong, G Hu, et al. "An analog simulation of stochastic resonance," ACTA Phys. SINICA, Vol. 41(3) , pp. 360-369, 1992．
180． B.R. Pamas, "Noise and neuronal populations conspire to encode simple waveforms reliably," IEEE Trans. Biomed. Eng., Vol. 43(3) , pp. 313-318, 1996．
181． S. Sancho & A. Suarez, "Nonlinear dynamics of microwave synthesizers-stability and noise", IEEE Trans.
Micro. Theory & Tech., Vol. 49(10) , pp. 1792-1803, 2001．
182． B. Ando, S. Baglio, "Measurements of parameters influencing the optimal noise level in stochastic systems," IEEE Trans. Instrumentation & Measurement, Vol. 49(5) , pp. 1137-1142,2000．
183． N. Hohn & A.N. Burkitt, "Modelling the neural response to speech: stochastic resonance and coding vowel-like stimuli," IEEE EMBS Confer. Monash University, pp. 1-4, 2001．
184． F. Chapeau-Blondeau, "Nonlinear test statistic to improve signal detection in non-Gaussian noise," IEEE Sig, Proc. Lett., Vol. 7(7) , pp. 205-207, 2000．
185． H. Papadopoulos, G Wornell & A.V. ppenheim, "Low-complexity digital encoding strategies for wireless sensor networks," Pro. IEEE Int. Conf. On Acoustics, Speech, and Signal Processing, pp. 3273-3276, 1998．
186． H. Papadopoulos & G Wornell, "A class of stochastic resonance systems for signal processing applications," Pro. IEEE Int. Conf. On Acoustics, Speech, and Signal Processing, Atlanta, GA, 1996．
187． H.E. Plesser & T. Geisel, "Bandpass properties of integrate-fire neurons," Neurocomputing, 26-27, pp.229-235, 1999．
188． A. Restrepo, L.F. Zuluaga & L.E. Pino, "Optimal noise levels for stochastic resonance," IEEE Int. Conf. On Acoustic, Speech and Signal Processing, Vol. 3, pp. 2365-2368, 1997．
189． N. Hohn & A.N. Burkitt, "Enhanced stochastic resonance in threshold detectors," Neural Network, IEEE Int. Confer. IJCNN'01, Vol. 1, pp. 644-647, 2001．
190． D.W. Repperger, C.A. Phillips & A. Neidhard, "A study on stochastic resonance involving the Hodgkin-Huxley Equation," Proceeding of the American Control Confer., Arlington, pp.229-231, 2001．
191． M. Lim & C. Saloma, "Noise-enhanced measurement of weak doublet spectra with a Fourier-transform spectrometer and 1-bit analog-to-digital converter," Applied Optics, Vol. 40( 11) , pp. 1767-1775, 2001．
192． H.C. Papadopoulos, GW. Wornell & A.V. Oppenheim, "Sequential Signal Encoding from Noisy Measurements Using Quantizers with Dynamic Bias Control," IEEE Trans. Inform. Theory, Vol. 47(3) , pp. 978-1002,2001．
193． F. Moss, "Stochastic resonance: a signal+noise in a two state system," Frequency Control, 1991． , Proceedings of the 45th Annual Symposium on, pp.649-658,1991．
194． A.R. Bulsara, F. Moss, "Single neuron dynamics: noise-enhanced signal processing," Neural Networks, 1991． 1991 IEEE International Joint Conference on, Vol. 1, pp. 420-425,1991．
195． S. Mizutani, T. Sano, & K. Shimohara, "Resonance in chaotic neural networks driven by a weak sinusoid," Neural Networks Proceedings, 1998． IEEE World Congress on Computational Intelligence. The 1998 IEEE InternationalJoint Conference on, Vol. 3, pp. 2551-2556,1998．
196． S. Mizutani, T. Sano, T. Uchiyama, et al. "Numerical studies of resonance in a sinusoidally driven chaotic neuron model and its network," Neural Networks 1997, Int. Con. on, Vol. 2, pp. 663-668, 1997．
197． H.A. Braun, H. Wissing, K. Schafer, et al. "Oscillation and noise determine signal transduction in shark multimodal sensory cells," Nature, Vol. 367, pp. 270-273, 1994．
198． S.M. Bezrukov & I Vodyanoy, "Noise-induced enhancement of signal transduction across vohage-dependent ion channels," Nature, Vol. 378, pp. 362-364, 1995．
199． R.P Morse & GF. Meyer, "The practical use of noise to improve speech coding by analogue cochlear implants," Chaos Solitons & Fractals, Vol. 11, pp. 1885-1894, 2000．
200． R.P. Morse & P. Roper, "Enhanced coding in a cochlear-implant model using additive noise: Aperiod stochastic resonance with tuning," Phys. Rev. E, Vol. 61(5) , pp. 5683-5692, 2000．
201． A.J. Matsuoka, J.T. Rubinstein, "The effects of interpulse interval on stochastic properities of electrical stimulation: Models and Measurements," IEEE Trans. Biomedical Eng,, Vol. 48(4) , pp. 416-424, 2001．
202． J.T.Rubinstein, B.S. Wilson, "Pseudospontaneous activity: stochastic independence of auditory nerve fibers
with electrical stimulation," Hearing Research, Vol. 127, pp. 108-118, 1999．
203． K.R. Henry & E.R. Lewis, "Cochlear nerve acoustic envelope response detection is improved by the addition of random-phased tonal stimuli," Hearing Research, Vol. 155, pp. 91-102, 2001．
204． F.G Zeng, Q.J. Fu & R. Morse, "Human hearing enhanced by noise," Brain Res., Vol. 869, pp. 251-255, 2000．
205． l.M. Collins, R.L. Miller & D. Ferguson, "On the relationship between noise and speech recognition in cochlear implant subjects: A theoretical and psychophysical study," Journal of the Acoustical Society of America, v 96, n 5 pt 1, Nov, p. 2731, 1994．
206． E. Lanzara, R.N. Mantegna, "Experimental study of a nonlinear system in the presence of noise; The stochastic resonance," Am. J. Phys., Vol. 65(4) , pp. 341-349,1997．
207． M. Locher, M.E. Inchiosa, "Theory of controlling stochastic resonance," Phys. Rev. E, Vol. 62(1) , pp. 317-327,2000．
208． B. Ando, S. Graziani, "A new IR displacement system based on noise added theory," Instrumentation and Measurement Technology Conference, 2001． IMTC 2001． Proceedings of the 18th IEEE, Vol. 1, pp. 482-485, 2001; B. Ando, S. Graziani, "Adding noise to improve measurement," IEEE Instrumentation & Measurement Magazine, Vol. 4(1) , pp.24-31, 2001． ; G Giuffrida, S. Graziani, N. Pitrone, "Signal recovery by using a QDW based approach," Instrumentation and Measurement Technology Conference, 2000． IMTC 2000． Proceedings of the 17th IEEE, Vol. 3, pp. 1512-1517, 2000． ; S. Baglio, S. Graziani, N. Pitrone, "Measurements of parameters influencing the optimal noise level in stochastic systems," Instrumentation and Measurement, IEEE Transactions on, Vol. 49(5) , pp. 1137-1143, 2000; S. Baglio, S. Graziani, N. Pitrone, "A system for the implementation of noise added system driving," Instrumentation and Measurement Technology Conference, 1999． IMTC/99． Proceedings of the 16th IEEE, Vol. 2, pp. 1059-1062, 1999; S. Baglio, S. Graziani, N. Pitrone, "A probabilistic approach to the threshold error reduction theory in bistable measurement devices," Instrumentation and Measurement Technology Conference, 1998． IMTC/98． Conference Proceedings. IEEE, Vol. 2, pp. 1307-1312, 1998． ; S. Baglio, S. Graziani, N. Pitrone, "Threshold error reduction in linear measurement devices by adding noise signal," Instrumentation and Measurement Technology Conference, 1998． IMTC/98． Conference Proceedings. IEEE, Vol. 1, pp. 42-46, 1998． ; N. Pitrone & S. Graziani, "Hysteresis Shaping in Stochastic Driven Systems," IEEE Trans INSTRUMENTATION & MEASUREMENT, Vol. 50(5) , pp. 1264-1269, 2001．
209． J. Tapson, "Stochastic resonance in a mode locked acoustic interferometer," Ultrasonics, Vol. 36, pp. 415-419, 1998．
210． L. Gammaitoni, M. Martinelli, "Stochastic resonance in paramagnetic resonance systems," J. Stat. Phys., Vol. 70(1-2) , pp. 425-435, 1993．
211． D. Petracchi, "What is the role of stochastic resonance?" Chaos, Solitons & Fractrals, Vol. 11, pp. 1827-1834,2000．
212． K. Loerincz, Z. Gingl & .L.B. Kiss, "A stochastic resonator is able to greatly improve signal-to-noise ratio," Phys. Lett. A, Vol. 224, pp. 63-67, 1996．
213． F. Chapeau-Blondeau, "Nonlinear test statistic to improve signal detection in non-Gaussian noise", IEEE Sig. Proc. Lett., Vol. 7(7) , pp. 205-207, 2000．
214． VS. Anishchenko, M.A. SAFONOVA & L.O. Chua, "Stochastic resonance in Chua's circuit driven by amplitude or frequency modulated signals," Int. J. Bifurcation & Chaos, Vol. 4(2) , pp. 441-446, 1994．
215． M. Morillo & J.G6mez-Ordonez, "Amplification and distortion of a period rectangular driving signal by a noisy bistable system", Phys. Rev. E, Vol. 51(2) , pp. 999-1003, 1995．
216． Proakis, J.G "Digital communications," Third Ed. New York: McGraw-Hill, pp.233-406, 1995．
217． Proakis, J.G & Salehi, M. "Contemporary communication systems using MATLAB," PWS Publishing company, 1997．
218． Schwartz, M. "Information transmission, modulation, and noise," Third Ed., McGraw-Hill, Inc., pp.390-570, 1980．
219． H. Risken, The Fokker-Planck Equation, Springer, New York, 1983．
220． B. Xu, F. Duan, R. Bao, et al. "Stochastic resonance with tuning system parameters: the application of bistable systems in signal processing," Chaos, Solitons & Fractals, Vol. 13(4) , pp. 633-644, 2002．
221． F. Duan & B. Xu, "Parameter-induced stochastic resonance and baseband binary PAM signal transmission over an AGWN channel," Int. J. Bifurcation & Chaos, Vol. 13(2) , 2003．
222． B. Xu, J. Li, F. Duan, et al. "Effects of colored noise on multi-frequency signal processing via stochastic resonance with tuning system parameters," Chaos, Solitons & Fractals, Vol. 16(1) , pp. 93-106,2003．
223． F. Duan, B. Xu, F. Chapeau-Blondeau, "Comparison of Stochastic Resonance via Adding Noise and That via Tuning System Parameters in Signal Transmission", Submitted to Phy. Rev. E.
224． J. Li, R. Bao, B. Xu, "Effects of some sort of nonlinear systems on signal processing via stochastic resonance with tuning system parameters," Accepted by Phys. A.
225． 段法兵，“参数调节随机共振在数字信号传输中的应用”，浙江大学博士论文。