混沌神经网络的同步控制及其应用
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摘要
混沌是当今前沿的研究课题，它揭示了自然界及人类社会中普遍存在的复杂性，反映了世界上无序和有序之间、确定性与随机性之间的辩证统一关系。混沌现象被称为与相对论、量子力学并列的20世纪三大物理学重要发现。二十世纪八十年代以来，混沌理论及其应用已成为非线性科学中的一个极其重要的分支。混沌的同步和控制是这一研究领域的一个热点问题，这一研究方向的深入开展为系统科学中的非线性现象提供了全新的认识。混沌系统所具有的复杂性、遍历性、不相关性、类噪声等特性，使得混沌控制和同步理论的研究极富挑战。本文围绕混沌同步和控制技术以及它们在现代信息安全保密方面的结合与应用这一课题，进行了较为广泛深入的研究。主要包括如下几个方面：
1．本文首先研究了Lorenz混沌系统的混沌控制方法。混沌控制是混沌领域的一个重要的研究课题，在不希望出现混沌的情形来消除动力系统中的混沌，可以通过混沌控制来实现。目前比较流行的混沌控制方法多来自于控制论，人们提出了很多有效地混沌控制策略。从应用角度来说，控制方案的设计要力求简单化，尽可能少地使用主系统状态变量构造简单的单个控制器来实现混沌系统的控制。本文结合反馈控制方法，提出了一种基于系统状态变量的错位线性控制器设计策略，用李雅普诺夫稳定性方法证明了该控制策略的稳定性，并设计了数值仿真算法验证了控制器的有效性。通过状态变量的相互作用实现稳定控制混沌的目的，控制器设计十分简单，易于实现。
2．在90年代初OGY方法首次实现混沌控制以来，混沌同步的研究逐步成为混沌研究的一个热点问题。非线性同步方法在混沌保密通信的应用方面有重要的理论意义，由于系统控制变量的非线性的特点，使得针对混沌混沌载波信号的攻击和破译更加困难，从理论上说，非线性全局同步方法可以提高混沌通信的保密性能，因此开展非线性同步方法的研究有重要的理论意义。本文研究了Lü提出的一个新的混沌系统的混沌同步问题，利用非线性反馈控制方法给出了三种混沌同步控制器设计方案，并用李雅普诺夫方法证明了在混沌控制器作用下，误差系统的稳定性。数值仿真结果表明，所设计的混沌控制器有效性和鲁棒性。接下来我们研究Lorenz超混沌系统的混沌同步问题，利用非线性反馈控制方法，给出了几个实现超混沌同步的控制器设计方案，结合李雅普诺夫稳定性理论证明了在混沌同步控制器作用下，驱动和相应混沌系统可以实现全局同步。数值仿真结果表明，所设计的混沌控制器能有效的实现混沌同步，并且具有很强的鲁棒性。
3．混沌是指在确定性系统中出现的一种貌似无规则的类似随机的现象。由于这个性质，使它可以被应用于科学的各个领域。近来人们发现混沌理论可以用来理解人脑中某些不规则的活动，因此对于混沌神经网络的研究也就成为摆在人们面前的又一新课题。混沌神经网络的这种复杂的动力学特性使它在信息处理和优化计算等方面有着广泛的应用前景。本文对混沌神经网络进行了深入的研究，介绍了混沌神经网络同步方法的发展及研究现状，基于线性矩阵不等式技术和李雅普诺夫稳定性理论，分别研究了全局同步、非线性全局同步和全局指数同步的同步控制器实现方法，提出了一种实现混沌神经网络同步的算法，通过该算法可以快速得到增益矩阵的形式，实现混沌系统的同步控制，数值仿真验证了算法的有效性。
4．利用混沌是目前混沌研究发展的一个重要方向，而混沌在通信领域的应用又是其中的一个热点问题。早期的同步混沌通信系统停留在低维混沌上，由于低维混沌动力学易于重构，混沌通信在抗破译能力上受到批评，同时通信效率的提高也受到很大限制。为了改进和提高保密通信的可靠性和稳定性，我们提出将超混沌系统的同步和混沌神经网络的同步用于保密通信，结合混沌遮掩通信，给出了基于混沌同步的保密通信新策略，数值仿真结果表明了算法的有效性。
Chaos is now a front research topic, it has promulgated the universal existence complexity in the nature and the human society, has reflected the dialectical unification relations in the world between disorderly and the order, definite and the random. Along with the theory of relativity and the quantum mechanics, chaos phenomenon is reputed as the third biggest physics discoveries in 20th century. Since 1980s, chaos theory and its application have become an important branch in the non-linear science field. The chaos synchronization and the control are the hot topics of this research area.The development of this research directs brand-new understanding of the non-linear phenomenon in dynamical systems. The complexity, ergodicity, aperiodic, uncorrelated, noise-like make the research on the chaotic control and synchronization theory to be morechallenging.
This article revolves the chaos synchronization and control technology as well as the application in the modern information security security aspect, main works and results include:
1. First we studied the chaos control method of Lorenz chaotic system. Chaos control is an important research topic. In the situation to eliminate chaos in the dynamic system, one can resort to the chaos control method. At present the quite popular chaos control method much comes from the cybernetics, people have proposed many effectively chaos control strategy. From the application view of point, the control scheme designed must make simplification and use the states variable of system as little as possible to realize the the chaos control, In this article, utilizing the feedback control method, we have proposed one kind linear controller design strategy based on the dislocation of the system states variable and proved the stability of the strategy with Lyapunov method. Then confirm the validity of the controller through simulation algorithm.Here we realized the stable control of chaos system through the mutual effect of state variable which is extremely simple and easy to realize.
2. Since the OGY method has realized the chaos control for the first time at the beginning of the 90's, the research of chaos synchronization becomes a hot topic field gradually. The non-linear synchronized method play an important role in the chaos secrete communication aspect. Because of the non-linear characteristic, it makes the attack and code breaks more difficultly. Theoretically speaking, the non-linear synchronization method may enhance the security of chaos communicaton performance.Therefore to development new non-linear synchronization method will make significance. Here we have studied the chaos synchronization of a new chaotic system. Based on nonlinear control method, three sufficient conditions of the controller for synchronization of the chaotic systems are derived. By means of Lyapunov stabilization theorem, it is proved that globally synchronization of the master and slave chaos system can be realized with the controller designed. Simulation results validate the proposed synchronization methods and show its robusticity. In the following, synchronization of hyperchaotic Lorenz system is studied. Based on nonlinear control method, several sufficient conditions of the controller for synchronization of the hyperchaotic Lorenz system are derived. By means of Lyapunov stabilization theorem, it is proved that globally synchronization of the master and slave chaos system can be realized with the controllers designed. Simulation results validate the proposed synchronization methods and show its robusticity.
3. The chaos is refers to one kind which appears in the definite system to apparent the non-rule the similar stochastic phenomenon. As a result of this nature, enables it possible to apply in science domain. Recently people have discovered that the chaos theory may use to understand certain irregular activities in the human brain, therefore chaos neural networks become an intensive research field. The complex dynamics characteristic of chaos neural network causes it prospective in information processing and optimized computation and other wide spread application. People have proposed many different control method to realize the chaos synchronization. This article has conducted the thorough research to the chaotic neural network, introduced the chaos neural network synchronization method. Based on the linear matrix inequality technology and Lyapunov stability theory, we have Studied the synchronized controller design method of the global synchronization, the non-linear global synchronization and the global exponential synchronization. Here we have proposed one kind of synchronization algorithm, through which might obtain the gain matrix quickly and automatize. Simulation has confirmed the validity of the algorithm.
4. Utilizing chaos is an important aspect during chaos development, in which the application is a hot topic. The early synchronized chaos communications system only focus on the lower chaotic system. Because the lowers chaoic dynamics are easy to restructure and attack, the chaos communication is under the criticism in ability of anti-breaks. Simultaneously the efficiency of chaos communication is not satisfied and need to improve. In order to improve the reliability and the stability of secure communication, we proposed to use the hyperchaotic system and the chaos neural network. With the chaos-mask communication, we gave a new strategy of secure communication based on the chaos synchronization. Simulation results show the validity of the algorithm.
1．本文首先研究了Lorenz混沌系统的混沌控制方法。混沌控制是混沌领域的一个重要的研究课题，在不希望出现混沌的情形来消除动力系统中的混沌，可以通过混沌控制来实现。目前比较流行的混沌控制方法多来自于控制论，人们提出了很多有效地混沌控制策略。从应用角度来说，控制方案的设计要力求简单化，尽可能少地使用主系统状态变量构造简单的单个控制器来实现混沌系统的控制。本文结合反馈控制方法，提出了一种基于系统状态变量的错位线性控制器设计策略，用李雅普诺夫稳定性方法证明了该控制策略的稳定性，并设计了数值仿真算法验证了控制器的有效性。通过状态变量的相互作用实现稳定控制混沌的目的，控制器设计十分简单，易于实现。
2．在90年代初OGY方法首次实现混沌控制以来，混沌同步的研究逐步成为混沌研究的一个热点问题。非线性同步方法在混沌保密通信的应用方面有重要的理论意义，由于系统控制变量的非线性的特点，使得针对混沌混沌载波信号的攻击和破译更加困难，从理论上说，非线性全局同步方法可以提高混沌通信的保密性能，因此开展非线性同步方法的研究有重要的理论意义。本文研究了Lü提出的一个新的混沌系统的混沌同步问题，利用非线性反馈控制方法给出了三种混沌同步控制器设计方案，并用李雅普诺夫方法证明了在混沌控制器作用下，误差系统的稳定性。数值仿真结果表明，所设计的混沌控制器有效性和鲁棒性。接下来我们研究Lorenz超混沌系统的混沌同步问题，利用非线性反馈控制方法，给出了几个实现超混沌同步的控制器设计方案，结合李雅普诺夫稳定性理论证明了在混沌同步控制器作用下，驱动和相应混沌系统可以实现全局同步。数值仿真结果表明，所设计的混沌控制器能有效的实现混沌同步，并且具有很强的鲁棒性。
3．混沌是指在确定性系统中出现的一种貌似无规则的类似随机的现象。由于这个性质，使它可以被应用于科学的各个领域。近来人们发现混沌理论可以用来理解人脑中某些不规则的活动，因此对于混沌神经网络的研究也就成为摆在人们面前的又一新课题。混沌神经网络的这种复杂的动力学特性使它在信息处理和优化计算等方面有着广泛的应用前景。本文对混沌神经网络进行了深入的研究，介绍了混沌神经网络同步方法的发展及研究现状，基于线性矩阵不等式技术和李雅普诺夫稳定性理论，分别研究了全局同步、非线性全局同步和全局指数同步的同步控制器实现方法，提出了一种实现混沌神经网络同步的算法，通过该算法可以快速得到增益矩阵的形式，实现混沌系统的同步控制，数值仿真验证了算法的有效性。
4．利用混沌是目前混沌研究发展的一个重要方向，而混沌在通信领域的应用又是其中的一个热点问题。早期的同步混沌通信系统停留在低维混沌上，由于低维混沌动力学易于重构，混沌通信在抗破译能力上受到批评，同时通信效率的提高也受到很大限制。为了改进和提高保密通信的可靠性和稳定性，我们提出将超混沌系统的同步和混沌神经网络的同步用于保密通信，结合混沌遮掩通信，给出了基于混沌同步的保密通信新策略，数值仿真结果表明了算法的有效性。
Chaos is now a front research topic, it has promulgated the universal existence complexity in the nature and the human society, has reflected the dialectical unification relations in the world between disorderly and the order, definite and the random. Along with the theory of relativity and the quantum mechanics, chaos phenomenon is reputed as the third biggest physics discoveries in 20th century. Since 1980s, chaos theory and its application have become an important branch in the non-linear science field. The chaos synchronization and the control are the hot topics of this research area.The development of this research directs brand-new understanding of the non-linear phenomenon in dynamical systems. The complexity, ergodicity, aperiodic, uncorrelated, noise-like make the research on the chaotic control and synchronization theory to be morechallenging.
This article revolves the chaos synchronization and control technology as well as the application in the modern information security security aspect, main works and results include:
1. First we studied the chaos control method of Lorenz chaotic system. Chaos control is an important research topic. In the situation to eliminate chaos in the dynamic system, one can resort to the chaos control method. At present the quite popular chaos control method much comes from the cybernetics, people have proposed many effectively chaos control strategy. From the application view of point, the control scheme designed must make simplification and use the states variable of system as little as possible to realize the the chaos control, In this article, utilizing the feedback control method, we have proposed one kind linear controller design strategy based on the dislocation of the system states variable and proved the stability of the strategy with Lyapunov method. Then confirm the validity of the controller through simulation algorithm.Here we realized the stable control of chaos system through the mutual effect of state variable which is extremely simple and easy to realize.
2. Since the OGY method has realized the chaos control for the first time at the beginning of the 90's, the research of chaos synchronization becomes a hot topic field gradually. The non-linear synchronized method play an important role in the chaos secrete communication aspect. Because of the non-linear characteristic, it makes the attack and code breaks more difficultly. Theoretically speaking, the non-linear synchronization method may enhance the security of chaos communicaton performance.Therefore to development new non-linear synchronization method will make significance. Here we have studied the chaos synchronization of a new chaotic system. Based on nonlinear control method, three sufficient conditions of the controller for synchronization of the chaotic systems are derived. By means of Lyapunov stabilization theorem, it is proved that globally synchronization of the master and slave chaos system can be realized with the controller designed. Simulation results validate the proposed synchronization methods and show its robusticity. In the following, synchronization of hyperchaotic Lorenz system is studied. Based on nonlinear control method, several sufficient conditions of the controller for synchronization of the hyperchaotic Lorenz system are derived. By means of Lyapunov stabilization theorem, it is proved that globally synchronization of the master and slave chaos system can be realized with the controllers designed. Simulation results validate the proposed synchronization methods and show its robusticity.
3. The chaos is refers to one kind which appears in the definite system to apparent the non-rule the similar stochastic phenomenon. As a result of this nature, enables it possible to apply in science domain. Recently people have discovered that the chaos theory may use to understand certain irregular activities in the human brain, therefore chaos neural networks become an intensive research field. The complex dynamics characteristic of chaos neural network causes it prospective in information processing and optimized computation and other wide spread application. People have proposed many different control method to realize the chaos synchronization. This article has conducted the thorough research to the chaotic neural network, introduced the chaos neural network synchronization method. Based on the linear matrix inequality technology and Lyapunov stability theory, we have Studied the synchronized controller design method of the global synchronization, the non-linear global synchronization and the global exponential synchronization. Here we have proposed one kind of synchronization algorithm, through which might obtain the gain matrix quickly and automatize. Simulation has confirmed the validity of the algorithm.
4. Utilizing chaos is an important aspect during chaos development, in which the application is a hot topic. The early synchronized chaos communications system only focus on the lower chaotic system. Because the lowers chaoic dynamics are easy to restructure and attack, the chaos communication is under the criticism in ability of anti-breaks. Simultaneously the efficiency of chaos communication is not satisfied and need to improve. In order to improve the reliability and the stability of secure communication, we proposed to use the hyperchaotic system and the chaos neural network. With the chaos-mask communication, we gave a new strategy of secure communication based on the chaos synchronization. Simulation results show the validity of the algorithm.
引文
[1] 方锦清．非线性系统中混沌的控制与同步及其应用前景[J]．物理学进展，1996,16：1-74．
[2] 崔春霞，吴锋民．控制周期激励Van der Pol-buffing振子的混沌[J]．浙江工业大学学报,2004,32：137-201．
[3] 吴祥兴，陈忠．混沌学导论[M]．上海：上海科学技术文献出版社，1996，85—98．
[4] 刘秉正．非线性动力学与混沌基础[M]．长春：东北师范大学出版社，1994,43—87．
[5] 郝柏林．从抛物线谈起—混沌动力学引论[M]．上海：上海科技教育出版社，1993，111-129．
[6] 邓伟谋，郝柏林．实用符号动力学[M]．上海：上海科技教育出版社，1994，16-37．
[7] 陈式刚．映象与混沌[M]．北京：国防工业出版社,1992，198—220
[8] Ott E., Grebogi C., York J. A. Controlling chaos [J]. Phys. Rev. Lett. 1990,64:1196-1199.
[9] Ditto W. D, Ranseo S.N, Spano M. L. Experimenial control of chaos [J]. Phys. Rev. Lett., 1990, 65: 3211-3214.
[10] Li T Y, Yorlce J A.Period three implies chaos [J].Am. Math Monthly, 1975, 82: 985-992.
[11] O. Diekmann, et. al. Delay Equations, functional complex nonlinear an.alysis[M]. Springer-Velger, New York, 1995
[12] G. Stepan, Retarded Dynamical Systems: Stability and Characteristic Functions [M]. Longman Scientific and Technical, 1989.
[13] Y. Kuang, Delay Differential Equations with Applications to Population Dynamics [M]. Academic Press, New York, 1993
[14] J. L. Moiola and G. Chen, Hopf Bifurcation Analysis: A Frequency Domain Approach [M]. World Scientific, Singapore, 1997.
[15] J. Gukenheimer, P. Holmes.Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields [M]. Springer-Verlag, New York, 1983.
[16] B. D. Hassard, D. Kazainof, Y. H. Wan.Theory and Applications of Hopf Bifurcations [M]. Cambridge University Press, Cambridge, 1981.
[17] G. Iooss,D. D. Joseph.Elementary Stability and Bifurcation Theory (2rid edition)[M].Springer -Verlag, New York, 1990.
[18] Pyragas K. Experimental control of chaos by delayed self- controlling feedback [J]. Phys. Lett.A, 1993, 180:99-102.
[19] Bleich M. E., Socolar J. E. S. Stability of periodic orbits controlled by time-delay feedback [J]. Phys. Lett. A, 1996, 210:87-94.
[20] Keill Konishi.Stability of extended delayed - feedback control for discrete time chaotic systems [J]. IEEE Trans. Circuits Syst. Ⅰ, 1999, 46:1285-1288.
[21] 刘锋等．一类混沌系统的非线性反馈控制[J]．控制和决策，2000，15：15—18．
[22] Holzhüter Th,,Klinker Th. Transient behavior for one-dimensional OGY control [J]. Int J Bifurcation and chaos, 2000, 10:1423-1435.
[23] Bemardo M. A purely adaptive controller to synchronize and control chaotic systems [J] . Phys Lett. A, 1996, 214:139-144.
[24] Zhang H. Z., Qin H. S.AdaPtive control of chaotic systems with uncertainties [J]. Int. J Bifurcation and chaos. 1998, 8: 2041-2046.
[25] Dong X., Chen L. AdaPtive control of the uncertain Duffing oscillator [J]. Int J Bifurcation and chaos. 1997, 7: 1651-1658.
[26] Alexander L.,Fradkov, Markov A. Yu.AdaPtive synchronization of chaotic systems based on speed gradient method and passification [J] .IEEE Trans, Circuits Syst, 1, 1997,44:905 -912.
[27] Tao Yang, Chun-Mei Yang and Lin-Bao Yang.A Detailed Study of Adaptive Control of Chaotic Systems with Unknown Pararneters [J]. Dynamics and Control. 1998, 8: 255-267.
[28] GE S. S., Wang C.Adaptive control of uncertain chus's cireuits [J]. IEEE Trans. Circuits Syst. 1, 2000, 47:1397-1402.
[29] Huberman B. A., Lumer E. Dynamics of adaptive systems [J].IEEE Trans. on Circuits and Systems, 1990, 37:547-550.
[30] Vassiliadis D. Parametric adaptive control and parameter identification of low-dimensional chaotic systems [J].Physica D, 1994, 71:319-341.
[31] Sinha S., Ramaswamy R., Rao J. S. Adaptive control in nonlinear dynamics [J]. Physica, D, 1990, 43:118-128.
[32] Oscar. Fuzzy control of chaos [J]. Int J Bifurcation and chaos, 1998, 8:1743-1747.
[33] Chen Liang, Chen Guanrong. Fuzzy modeling and adaptive control of uncertain chaotic systems [J]. Information Sciences, 1999, 121- :27-37.
[34] Chen Liang, Chen Guanrong. Fuzzy predictive control of uncertain chaotic systems using time series [J]. Int J Bifurcation and chaos, 1999, 9:757-767.
[35] Chen Liang, Chen Guanrong. Fuzzy modeling, prediction, and control of uncertain chaotic systems based on time series [J]. IEEE Trans. Circuits Syst. Ⅰ, 2000, 47:1527-1531.
[36] Arecchi F. T. The control of chaos: theoretical schemes and experimental realizations [J]. Int J Bifurcation and chaos. 1998, 8:1643-1655.
[37] Guo mei, Shien Leang S., Chne Guanrong. Ordering chaos in chua's circuit: a sampled-data feedback and digital-data feedback and digital redesign approach [J]. Int J Bifurcation and chaos, 2000, 10:2221-2231.
[38] Poznyak A. S., Yu wen, Sanchez E. N. Identification and control of unknown chaotic systems viadynamic neural networks [J]. IEEE Trans. Circuits Syst. Ⅰ, 1999, 46:1491-1495.
[39] Lin Chinteng. Controlling chaos by GA - based reinforcement learning neural network [J]. IEEE Trans On neural networks, 1999, 10:846 - 859.
[40] ChinTeng Lin. Controlling chaos by GA - based reinforcement learning neural network [J]. IEEE Trans. on neural networks, 1999, 10: 846- 859.
[41] Poznyak A.S, Sanchez E. N.Identification and control of unkmown chaotic systems via dynamic neural netorks [J]. IEEE Trans. Cireuits Syst. 1, 1999, 46:1491 -1495.
[42] 王忠勇，蔡远利，贾冬等．混沌系统的神经网络控制[J]．控制与决策，2000，15：55-58．
[43] Pecora L.M., Carroll T. L.On the control and synchronization of chaos [J].Phys. Rev. Lett. 1990, 64:821-827.
[44] Pecora L M, Carroll T. C. synchronization in chaotic system [J]. Phys. Rev. Lett. 1990, 64: 821-824.
[45] Guo P.J., Wallace K.S. A global synchronization criterion for coupled chaotic systems via unidirectional linear error feedback approach [J]. Int. J .Bifurcat. Chaos 2002,12:2239 - 2253.
[46] Pecora L.M., Carroll T.L. Synchronization in chaotic systems. Phys. Rev. Lett. 1990,64:821 - 4.
[47] Sprott JC. A new class of chaotic circuits [J]. Phys. Lett. A 2000,266:19 - 23.
[48] Sarasola C. Feedback synchronization of chaotic systems. Int J Bifurcat Chaos 2003,13:177 - 91.
[49] Yang T., Shao H. H. Synchronizing chaotic dynamics with uncertainties based on a sliding mode control design. Phys. Rev. E 2002,65: 46-210.
[50] Utkin Ⅵ. Sliding modes in control and optimization [M]. Berlin: Springer-Verlag, 1992.
[51] Cuomo KM, Oppenheim A V. Circuit Implementation of Synchronized Chaos with Applications to Communication [J]. Phy. Rev. Lett., 1993, 71: 65-68.
[52] 刘峰，等．混沌系统的反馈同步及其在保密通信中的应用[J]．电子学报，2000，28：46-48．
[53] T.L. Liao, N.S. Huang. An Observed2Based Approach for Chaotic Synchronization with Applications to Secure Communications [J]. IEEE Trans. on CAS-Ⅰ, 1999, 46:1144-1150.
[54] Changsong Zhou. Extracting Messages Masked by Chaotic Signals of Time-Delay Systems [J]. Phys. Rev. E, 1999,60:320-323.
[55] 李建芬，李农．一种新的蔡氏混沌掩盖通信方法[J]．系统工程与电子技术，2002，24：41-43．
[56] Lorenz, E. N., Deterministic nonperiodic flow [J].J. Atmos. Sci., 1963, 20:130-141.
[57] Schuster H.G, Stemmler M.B.Control of chaos by oscillating feedback [J]. Phys. Rev. E 1997, 56:6410-3417.
[58] Koumboulis F.N., Mertzios B.G Feedback controlling against chaos [J]. Chaos, Solitons & Fractals 2000, 11:351-358.
[59] Chen G, Dong X .From chaos to order: methodologies, perspectives and applications [M]. Singapore: World Scientific, 1998.
[60] Chen G, Yu X. On time-delayed feedback control of chaotic systems [J]. IEEE Trans. Circ. Syst. I 1999,46:767-72.
[61] Galias Z, Murphy CA, Kennedy MP, Ogorzalek MJ. Electronic chaos controller [J]. Chaos, Solitons & Fractals, 1997, 8:1471-1484.
[62] Park J. H.Controlling chaotic systems via nonlinear feedback control [J].Chaos, Solition & Fractals, 2005, 23:1049-1054.
[63] X Yu. Controlling chaos using input-output linearization approach [J]. Int J Bifurcation and Chaos, 1997,7: 1664-95.
[64] C. J. Wand, Sbernstein. Nonlinear feedback control with global stabilization [J]. Dyn. Contr. 1995,5:321-46.
[65] Yu X. Controlling Lorenz chaos [J]. Int J of Systems Science 1996, 27:355-359.
[66] Sevedo M, Giuseppe G. Controlling chaotic dynamics using backstepping design with application to the Lorenz system and Chua's circuit [J].Int J Bifurcation and Chaos 1999, 9:1425-1434.
[67]X.Yu.Variable structure control approach for. Controlling chaos [J]. Chaos, Solitons and Fractals,1997,9:1577-1586.
[68] Chen G, Ueta T. Yet another chaotic attractor [J]. Int J Bifurcation Chaos, 1999, 9: 1465-1466.
[69] Lu J, Zhou T, Zhang S. Chaos synchronization between linearly coupled chaotic system [J].Chaos, Solition & Fractals, 2002, 14:529-541.
[70] Roy R., Murphy T. W. Dynamical control of a chaotic laser: Experimental stabilization of a globally coupled system [J]. Physical Review Letters, 1992, 68):1259-1262.
[71] Dykstra, R., Tang, D.Y., Heckenberg, N. R. Experimental control of a single mode laser chaos by using continuous time delayed feedback [J]. Phys Rev E, 1998, 57: 6596-6598.
[72] Zhang J. S., Xiao X. C.Fast evolving Multi-layer perceptions for noisy chaotic time series modeling and predictions [J]. Chin Phys, 2000, 9:408-413.
[73] Lii J. H., Zhou T. S. Controlling the Chen attractor using linear feedback based on parameter identification [J]. Chin Phys, 2002, 11:12-16.
[74] Kocarev L, Parliza V. General approach for chaotic synchronization with application to commu- nication [J]. Physical Review Letters, 1995, 74:5028-5031.
[75] Matsumoto T., Chua L. O., Kobayashi K. Hyperchaos: laboratory experiment and numerical confirmation [J].IEEE Transactions on CAS, 1986, 33:1143-1147.
[76] Brucoli M., Carnimeo L., Grassi G.A method for the synchronization of hyperchaoticc ircuits[J].Int J Bifurcation and chaos, 1996,6:1673-1681.
[77] Grassi G, Mascolo.Nonlinear observer design to synchronize hyperchaotic systems via a scalar signal [J].IEEE Transactions on CAS-Ⅰ: Fundamental Theory and Applications,1997, 4:1011-1014.
[78] Wang T.B, Tan T.F. Coupled synchronization of hyperchaotic systems[J].Acta Physica Sinica,2001,50:1851-1855.
[79] Xiaofeng Liao, Zhongfu, and Juebang Yu, Hopf bifurcation analysis of a neural system with a continuously distributed delay[C], International Symposium on Signal Processing and Intelligent System, Guangzhou, China, 1999:546-549.
[80] Xiaofeng Liao, Zhongfu and Juebang Yu, Stability switches and bifurcation analysis of a neural network with continuously distributed delay [J].IEEE Trans. On SMC-Ⅰ, 1999, 29:692-696.
[81] K. Gopalsamy, I. Leung, Delay induced periodicity in a neural network of excitation and inhibition [J]. Physica D,1996, 89:395-426.
[82] 廖晓峰，吴中福，虞厥邦．带分布时延神经网络：从稳定到振荡再到稳定的动力学现象[J]．电子与信息学报，2001，23：689-692．
[83] Xiaofeng Liao, Kwok-wo Wong, Zhongfu Wu, Bifurcation analysis in a two-neuron system with continuously distributed delays. Physica D, 2001, 179:123-141.
[84] 靳藩编著．神经计算智能基础[M]．成都：西南交通大学出版社，2000．
[85] K. Murali, M. Lakshmanan, and L. O. Chua. The Simplest Dissipative Nonautonomous Chaotic Circuit [J]. IEEE Trans. on CAS-Ⅰ: Fundamental Theory and Applications. 1994, 41:462-463.
[86] Hongtao Lu, Yongbao He, and Zhenya He. A Chaos-Generator: Analyses of Complex Dynamics of a Cell Equation in Delayed Cellular Neural Networks [J]. IEEE Trans. on CAS-Ⅰ: Fundamental Theory and Applications. 1998, 45:178-181.
[87] Marco Gilli. Strange Attractors in Delayed Cellular Neural Networks [J]. IEEE Trans, on CAS-I:Fundamental Theory and Applications. 1993, 40:849-853.
[88] Hongtao Lu and Zhenya He. Chaotic Behavior in First-Order Autonomous Continuous-Time Systems with Delay [J]. IEEE Trans, on CAS-I: Fundamental Theory and Applications. 1996,43:699-702.
[89] K. Gopalsamy and Issic K. C. Leung. Convergence under Dynamical Thresholds with Delay [J].IEEE Trans, on Neural Networks. 1997, 8:341-348.
[90] J. Belair, S. Dufour. Stability in a three-dimensional system of delay-differential equations [J].Can. Appl. Math. Quart., 1996, 4:135-156.
[91] L. Olien, J. Belair, Bifurcations.Stability and monotonicity properties of a delayed neural network model [J], Physica D, 1997, 102:349-363.
[92] Aihara K, et al. Chaotic Neural Networks [J]. Phys. Lett. A, 1990, 144: 334-340.
[93] J. Belair, et. al., Frustration, Stability, and Delay-Induced Oscillations in a Neural Network Model [J]. SIAM Journal on Applied Mathematics, 1996, 56:245-255
[94] L.O. Chua, CNN: A Paradigm for Complexity [M]. World Scientific, Singapore, 1998.
[95] L.O. Chua, L. Yang, IEEE'Trans. Circuits Systems, 1988, 35:1273-1285.
[96] Nozawa H. A Neural - network Model as a Globally Coupled Map and Application Based on Chaos [J]. Chaos, 1992, 3:3140-3145.
[97] Inoue M, Nagayoshi A. A Chaos Neuro- computer [J ].Phys. Lett. A ., 1991 , 8 :373 - 76.
[98] R. J. Wang and W. J. Wang. Stability Analysis of Perturbed Systems with Multiple Noncommensurate Time Delays [J]. IEEE Trans. Circuits & Systems-I, 1996, 43:349-352.
[99] Y. J. Sun, et. al. On the Stability of Uncertain Systems with Multiple Time-Varying Delays [J].IEEE Transaction on Automatic Control, 1997, 42:101-105.
[100] H. S. Wu and K. Mizukami. New Sufficient Conditions for Robust Stability of Time-Delay Systems with Structured State Space Uncertainties[J].Transactions of the Society of Information Control Electronics, 1996, 32:336-344.
[101] J. Belair and S. A. Campell, Stability and Bifurcations of Equilibria in a Multiple-Delayed Differential Equation [J].SIAM J. Appl. Math., 1994, 54:1402-1424.
[102] S. A. Compell, et. al, Complex Dynamics and Multistability in a Damped Harmonic Oscillator with Delayed Negative Feedback[J].Chaos, 1995, 5:640-645.
[103] N. MacDonald, Harmonic Balance in Delay-Differential Equations [J].Journal of Sound and Vibration, 1995, 186:649-656.
[104] K. Sato et. al, Dynamic Motion of a Nonlinear Mechanical System with Time Delay (Analysis of the Self-Excited Vibration by an Averaging Method) [J], Transactions of Japanese Society of Mechanical Engineering, Series C, 1995, 61 :1855-1860.
[105] K. Sato et. al. Dynamic Motion of a Nonlinear Mechanical System with Time Delay (Analysis of the Forced Vibration by an Averaging Method) [J], Trans. JSME, Series C,1995,61:1861-1866.
[106] J. S. Lin and C. I. Weng.A Nonlinear Dynamic Model of Cutting [J].Int. J. Mach. Tools Manufact, 1990,30:53-64.
[107] Y. Tsuda, et. al., Chaotic Behavior of a Nonlinear Vibrating System with a Retarded Argument (Characteristics in the Region of Subharmonics Resonance) [J], Trans. JSME, Series C, 1993,59:2425-2432.
[108] E. Boe, H. C. Chang.Transition to Chaos from a two-torus in a delayed feedback system [J].Int.J. of Bifur. Chaos, 1991, 1:67-81.
[109] Y.Ueda, H.Ohta, H.B.Stewart.Bifurcation in a System Described by a Nonlinear Differential Equation with Delay [J], Chaos, 1994,4:75-83.
[110] K.Ikeda,K. Matsumoto.High-Dimensional Chaotic Behavior in Systems with Time-Delayed Feedback[J].Physica D, 1987, 29:223-235.
[111] S. Lepri, et.al, High-Dimensional Chaos in Delayed Dynamical Systems [J], Physica D, 1993,70:235-249.
[112] W. Just, et.al.Mechanism of Time-Delayed Feedback Control [J], Physical Review Letters, 1997, 78:203-206.
[113] P.Celka.Control of Time-Delayed Feedback Systems with Application to Optics [J],International Journal of Electronics, 1995, 79:787-795.
[114] J. E. S. Socolar, et.al., Stabilizing Unstable Periodic Orbits in Fast Dynamical Systems [J],Physics Reviews E, 1994, 50:3245-3248.
[115] K. Pyragas, Control of Chaos via Extended Delay Feedback [J], Phys. Lett. A, 1995,206:323-330.
[116] A. Kittle et.al. Delayed Feedback Control of Chaos by Self-Adapted Delay Time [J], Phys. Lett.A, 1995, 198:433-436.
[117] H. Nakajima, etal.Automatic Adjustment of Delay Time and Feedback Gain in Delayed Feedback Control of Chaos [J], IEICE Trans. Fundamentals, 1997, 9:1554-1559.
[118] Y. Tsuda, et. aL.On the Chaotic Behavior of Asymmetrical Duffing Oscillators [J], Trans. JSME,Series C, 1992,58:731-737.
[119] S. Boyd, L.EI. Ghaoui, E. Feron, V. Balakrishnan.Linear Matrix Inequalities in System and Control Theory [M]. SIAM, Philadelphia, PA, 1994.
[120] Skelton R. E., Iwasaki T. Increased roles of linear algebra in control education [J]. IEEE Control Syst. Mag., 1995, 15:76-89.
[121 ] Vandenberghe L ,Boyd S. Semidefinite programming [J]. SIAM Review, 1996, 38: 49-95.
[122] Balakrishnan V ,Feron E . Linear Matrix Inequalities in Control Theory and aplications [J].special issue of the Int. J. Robust and Nonlinear Control, 1996, 6: 896-1099.
[123] Balakrishnan V. ,Kashyap R L. Robust stability and performance analysis of uncertain systems using linear matrix inequalities [J]. J Optimization Theory and Applications, 1999, 100:457-478.
[124] Jeremy G. V., Braatz R. D. A tutorial on linear and bilinear matrix inequalities [J]. J. Process Control, 2000, 10:63-385.
[125] EI Ghaoui L , Niculescu S I. Advances in Matrix Inequality Methods in Control [M]. Advances in Design and Control. Philadelphia: SIAM, 2000.
[126] P. Gahinet, A. Nemirovskii, A.J. Laub, M. Chilali, LMI Control Toolbox User's Guide[M] The Math Works Inc., Natick, MA, 1995.
[127] Karmarkar N. K. A new polynomial-time algorithm for linear programming [J]. Combinatorica,1984, 4:373-395.
[128] Nesterov Y , Nemirovsky A. Interior-point polynomial methods in convex programming [M].Philadelphia: SIAM, 1994.
[129]Alizadeh F. Interior-point methods in semidefinite programming with applications to combinatorial optimization [J]. SIAM J. Optimization, 1995, 5: 13-51.
[130]T. Roska, L.O. Chua.Cellular neural networks with nonlinear and delay-type template [J].Int. J.Circuit Theory Appl., 1992, 20:469-481.
[131]C.M. Marcus, R.M, Westervelt.Stability of analog neural networks with delay [J]. Phys. Rev. A.,1989,39:347-359.
[132]M. Cohen, S. Grossberg.Absolute stability and global pattern formation and parallel memory storage by competitive neural networks [J]. IEEE Trans. Syst. Man Cybern, 1983, 13:815 - 826.
[133]P. van den Diressche, X. Zou, .Global attractivity in delayed Hopfield neural network models [J].SIAM J. Appl.Math., 1998, 58:1878 - 1890.
[134]J.D. Cao.Global exponential stability of Hopfield neural networks [J]. International Journal of Systems Science,2001,32:233 - 236.
[135]J.D. Cao, J. Wang. Absolute exponential stability of recurrent neural networks with Lipschitz-con tinuous activation functions and time delays[J].Neural Networks, 2004,17:379 - 390.
[136]H. Ye, A.N. Michel, K. Wang.Global stabilityand local stabilityof Hopfield neural networks with delays [J]. Phys. Rev. E, 1994, 50: 4206 - 4213.
[137]Y. Zhang, P.A. Heng, K.S. Leung.Convergence analysis of cellular neural networks with unbounded delay [J]. IEEE Trans. Circuits and Systems I, 2001, 48:680 - 687.
[138]Zou F, Nossek J.A.A chaotic attractor with cellular neural networks [J]. IEEE Trans. Circ. Syst. I,1991,38:811-812.
[139]Zou F, Nossek J.A.Bifurcation and chaos in cellular neural networks [J]. IEEE Trans. Circ. Syst. 1,1993,40:166-173.
[140]Gilli M.Strange attractors in delayed cellular neural networks[J].IEEE Trans.Circ.Syst.I,1993,40,:849-853.
[141]Lu H.T.Chaotic attractors in delayed neural networks [J].Phys. Lett. A, 2002,298:109 - 116.
[142]Lu H.T, He Z.Y.Chaotic behavior in first-order autonomous continuous-time systems with delay [J]. IEEE Trans. Circ. Syst. I, 1996,43:700 - 702.
[143]G.R. Chen, J. Zhou, Z.R. Liu.Global synchronization of coupled delayed neural networks and applications to chaotic CNN model [J].Int. J. Bifur. Chaos, 2004,14:2229 - 2240.
[144]C.W. Wu, L.O. Chua.Synchronization in an array of linearly coupled dynamical system [J].IEEE Trans. Circuit.Syst. I, 1995,42:430 - 447.
[145] W.L. Lu, T.P. Chen.Synchronization of coupled connected neural networks with delays [J]. IEEE Trans. Circuits. Syst. I, 2004,51:2491 - 2503.
[146]S. Mohamad, K. Gopalsamy.Exponential stability of continuous-time and discrete-time cellular neural networks with delays [J]. Appl. Math. Comput, 2003, 135:17-30.
[147]Q. Dong, K. Matsui, X. Huang.Existence and stability of periodic solutions for Hopfield neural network equations with periodic input[J] .Nonlinear Anal, 2002,49:471-479,.
[148]C.J. Cheng, T.L. Liao, C.C. Hwang, "Exponential synchronization of a class of chaotic neural networks," Chaos, Solitons and Fractals, 2005,24:197 - 206,.
[149] Gopalsamy K. Stability and oscillations in delay differential equations of population dynamics [M]. The Netherlands: Kluwer Academic Publishers, 1992.
[150] S.Xu, T.Chen, J.Lam.Robust H∞ filtering for uncertain Markovian jump systems with mode-dependent time delays[J ].IEEE Trans. Automat. Control, 2003,48 (5):900-907.
[151]Cao Jinde, Ho.Daniel W.C.A general framework for global asymptotic stability analysis of delayed neural networks based on LMI approach [J].Chaos Solitons and Fractals,2005,24 (5):1317-1329
[152] S.Boyd, L. E.Ghaoui, E.Feron, V.Balakrishnan. Linear Matrix Inequalities in System and Control Theory [M], SIAM, Philadelphia, PA, 1994.
[153] Halle K. S., Wu C.W. Spread spectrum communication through modulation of chaos in chua's circuit .Singapore: World scientific, 1993, 379-394
[154] 何思远等．混沌掩盖的同步通信技术[J]．沈阳航空工业学院学报，2005，22(5)：61-62．
[155] 张亚兵．混沌系统的同步及其在通信中的应用[D]．南京理工大学，2003．
[156] 蒋国平，王锁萍．细胞神经网络超混沌系统同步及其在保密通信中应用[J]．通信学报，2000，21(9)：79-85．
[2] 崔春霞，吴锋民．控制周期激励Van der Pol-buffing振子的混沌[J]．浙江工业大学学报,2004,32：137-201．
[3] 吴祥兴，陈忠．混沌学导论[M]．上海：上海科学技术文献出版社，1996，85—98．
[4] 刘秉正．非线性动力学与混沌基础[M]．长春：东北师范大学出版社，1994,43—87．
[5] 郝柏林．从抛物线谈起—混沌动力学引论[M]．上海：上海科技教育出版社，1993，111-129．
[6] 邓伟谋，郝柏林．实用符号动力学[M]．上海：上海科技教育出版社，1994，16-37．
[7] 陈式刚．映象与混沌[M]．北京：国防工业出版社,1992，198—220
[8] Ott E., Grebogi C., York J. A. Controlling chaos [J]. Phys. Rev. Lett. 1990,64:1196-1199.
[9] Ditto W. D, Ranseo S.N, Spano M. L. Experimenial control of chaos [J]. Phys. Rev. Lett., 1990, 65: 3211-3214.
[10] Li T Y, Yorlce J A.Period three implies chaos [J].Am. Math Monthly, 1975, 82: 985-992.
[11] O. Diekmann, et. al. Delay Equations, functional complex nonlinear an.alysis[M]. Springer-Velger, New York, 1995
[12] G. Stepan, Retarded Dynamical Systems: Stability and Characteristic Functions [M]. Longman Scientific and Technical, 1989.
[13] Y. Kuang, Delay Differential Equations with Applications to Population Dynamics [M]. Academic Press, New York, 1993
[14] J. L. Moiola and G. Chen, Hopf Bifurcation Analysis: A Frequency Domain Approach [M]. World Scientific, Singapore, 1997.
[15] J. Gukenheimer, P. Holmes.Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields [M]. Springer-Verlag, New York, 1983.
[16] B. D. Hassard, D. Kazainof, Y. H. Wan.Theory and Applications of Hopf Bifurcations [M]. Cambridge University Press, Cambridge, 1981.
[17] G. Iooss,D. D. Joseph.Elementary Stability and Bifurcation Theory (2rid edition)[M].Springer -Verlag, New York, 1990.
[18] Pyragas K. Experimental control of chaos by delayed self- controlling feedback [J]. Phys. Lett.A, 1993, 180:99-102.
[19] Bleich M. E., Socolar J. E. S. Stability of periodic orbits controlled by time-delay feedback [J]. Phys. Lett. A, 1996, 210:87-94.
[20] Keill Konishi.Stability of extended delayed - feedback control for discrete time chaotic systems [J]. IEEE Trans. Circuits Syst. Ⅰ, 1999, 46:1285-1288.
[21] 刘锋等．一类混沌系统的非线性反馈控制[J]．控制和决策，2000，15：15—18．
[22] Holzhüter Th,,Klinker Th. Transient behavior for one-dimensional OGY control [J]. Int J Bifurcation and chaos, 2000, 10:1423-1435.
[23] Bemardo M. A purely adaptive controller to synchronize and control chaotic systems [J] . Phys Lett. A, 1996, 214:139-144.
[24] Zhang H. Z., Qin H. S.AdaPtive control of chaotic systems with uncertainties [J]. Int. J Bifurcation and chaos. 1998, 8: 2041-2046.
[25] Dong X., Chen L. AdaPtive control of the uncertain Duffing oscillator [J]. Int J Bifurcation and chaos. 1997, 7: 1651-1658.
[26] Alexander L.,Fradkov, Markov A. Yu.AdaPtive synchronization of chaotic systems based on speed gradient method and passification [J] .IEEE Trans, Circuits Syst, 1, 1997,44:905 -912.
[27] Tao Yang, Chun-Mei Yang and Lin-Bao Yang.A Detailed Study of Adaptive Control of Chaotic Systems with Unknown Pararneters [J]. Dynamics and Control. 1998, 8: 255-267.
[28] GE S. S., Wang C.Adaptive control of uncertain chus's cireuits [J]. IEEE Trans. Circuits Syst. 1, 2000, 47:1397-1402.
[29] Huberman B. A., Lumer E. Dynamics of adaptive systems [J].IEEE Trans. on Circuits and Systems, 1990, 37:547-550.
[30] Vassiliadis D. Parametric adaptive control and parameter identification of low-dimensional chaotic systems [J].Physica D, 1994, 71:319-341.
[31] Sinha S., Ramaswamy R., Rao J. S. Adaptive control in nonlinear dynamics [J]. Physica, D, 1990, 43:118-128.
[32] Oscar. Fuzzy control of chaos [J]. Int J Bifurcation and chaos, 1998, 8:1743-1747.
[33] Chen Liang, Chen Guanrong. Fuzzy modeling and adaptive control of uncertain chaotic systems [J]. Information Sciences, 1999, 121- :27-37.
[34] Chen Liang, Chen Guanrong. Fuzzy predictive control of uncertain chaotic systems using time series [J]. Int J Bifurcation and chaos, 1999, 9:757-767.
[35] Chen Liang, Chen Guanrong. Fuzzy modeling, prediction, and control of uncertain chaotic systems based on time series [J]. IEEE Trans. Circuits Syst. Ⅰ, 2000, 47:1527-1531.
[36] Arecchi F. T. The control of chaos: theoretical schemes and experimental realizations [J]. Int J Bifurcation and chaos. 1998, 8:1643-1655.
[37] Guo mei, Shien Leang S., Chne Guanrong. Ordering chaos in chua's circuit: a sampled-data feedback and digital-data feedback and digital redesign approach [J]. Int J Bifurcation and chaos, 2000, 10:2221-2231.
[38] Poznyak A. S., Yu wen, Sanchez E. N. Identification and control of unknown chaotic systems viadynamic neural networks [J]. IEEE Trans. Circuits Syst. Ⅰ, 1999, 46:1491-1495.
[39] Lin Chinteng. Controlling chaos by GA - based reinforcement learning neural network [J]. IEEE Trans On neural networks, 1999, 10:846 - 859.
[40] ChinTeng Lin. Controlling chaos by GA - based reinforcement learning neural network [J]. IEEE Trans. on neural networks, 1999, 10: 846- 859.
[41] Poznyak A.S, Sanchez E. N.Identification and control of unkmown chaotic systems via dynamic neural netorks [J]. IEEE Trans. Cireuits Syst. 1, 1999, 46:1491 -1495.
[42] 王忠勇，蔡远利，贾冬等．混沌系统的神经网络控制[J]．控制与决策，2000，15：55-58．
[43] Pecora L.M., Carroll T. L.On the control and synchronization of chaos [J].Phys. Rev. Lett. 1990, 64:821-827.
[44] Pecora L M, Carroll T. C. synchronization in chaotic system [J]. Phys. Rev. Lett. 1990, 64: 821-824.
[45] Guo P.J., Wallace K.S. A global synchronization criterion for coupled chaotic systems via unidirectional linear error feedback approach [J]. Int. J .Bifurcat. Chaos 2002,12:2239 - 2253.
[46] Pecora L.M., Carroll T.L. Synchronization in chaotic systems. Phys. Rev. Lett. 1990,64:821 - 4.
[47] Sprott JC. A new class of chaotic circuits [J]. Phys. Lett. A 2000,266:19 - 23.
[48] Sarasola C. Feedback synchronization of chaotic systems. Int J Bifurcat Chaos 2003,13:177 - 91.
[49] Yang T., Shao H. H. Synchronizing chaotic dynamics with uncertainties based on a sliding mode control design. Phys. Rev. E 2002,65: 46-210.
[50] Utkin Ⅵ. Sliding modes in control and optimization [M]. Berlin: Springer-Verlag, 1992.
[51] Cuomo KM, Oppenheim A V. Circuit Implementation of Synchronized Chaos with Applications to Communication [J]. Phy. Rev. Lett., 1993, 71: 65-68.
[52] 刘峰，等．混沌系统的反馈同步及其在保密通信中的应用[J]．电子学报，2000，28：46-48．
[53] T.L. Liao, N.S. Huang. An Observed2Based Approach for Chaotic Synchronization with Applications to Secure Communications [J]. IEEE Trans. on CAS-Ⅰ, 1999, 46:1144-1150.
[54] Changsong Zhou. Extracting Messages Masked by Chaotic Signals of Time-Delay Systems [J]. Phys. Rev. E, 1999,60:320-323.
[55] 李建芬，李农．一种新的蔡氏混沌掩盖通信方法[J]．系统工程与电子技术，2002，24：41-43．
[56] Lorenz, E. N., Deterministic nonperiodic flow [J].J. Atmos. Sci., 1963, 20:130-141.
[57] Schuster H.G, Stemmler M.B.Control of chaos by oscillating feedback [J]. Phys. Rev. E 1997, 56:6410-3417.
[58] Koumboulis F.N., Mertzios B.G Feedback controlling against chaos [J]. Chaos, Solitons & Fractals 2000, 11:351-358.
[59] Chen G, Dong X .From chaos to order: methodologies, perspectives and applications [M]. Singapore: World Scientific, 1998.
[60] Chen G, Yu X. On time-delayed feedback control of chaotic systems [J]. IEEE Trans. Circ. Syst. I 1999,46:767-72.
[61] Galias Z, Murphy CA, Kennedy MP, Ogorzalek MJ. Electronic chaos controller [J]. Chaos, Solitons & Fractals, 1997, 8:1471-1484.
[62] Park J. H.Controlling chaotic systems via nonlinear feedback control [J].Chaos, Solition & Fractals, 2005, 23:1049-1054.
[63] X Yu. Controlling chaos using input-output linearization approach [J]. Int J Bifurcation and Chaos, 1997,7: 1664-95.
[64] C. J. Wand, Sbernstein. Nonlinear feedback control with global stabilization [J]. Dyn. Contr. 1995,5:321-46.
[65] Yu X. Controlling Lorenz chaos [J]. Int J of Systems Science 1996, 27:355-359.
[66] Sevedo M, Giuseppe G. Controlling chaotic dynamics using backstepping design with application to the Lorenz system and Chua's circuit [J].Int J Bifurcation and Chaos 1999, 9:1425-1434.
[67]X.Yu.Variable structure control approach for. Controlling chaos [J]. Chaos, Solitons and Fractals,1997,9:1577-1586.
[68] Chen G, Ueta T. Yet another chaotic attractor [J]. Int J Bifurcation Chaos, 1999, 9: 1465-1466.
[69] Lu J, Zhou T, Zhang S. Chaos synchronization between linearly coupled chaotic system [J].Chaos, Solition & Fractals, 2002, 14:529-541.
[70] Roy R., Murphy T. W. Dynamical control of a chaotic laser: Experimental stabilization of a globally coupled system [J]. Physical Review Letters, 1992, 68):1259-1262.
[71] Dykstra, R., Tang, D.Y., Heckenberg, N. R. Experimental control of a single mode laser chaos by using continuous time delayed feedback [J]. Phys Rev E, 1998, 57: 6596-6598.
[72] Zhang J. S., Xiao X. C.Fast evolving Multi-layer perceptions for noisy chaotic time series modeling and predictions [J]. Chin Phys, 2000, 9:408-413.
[73] Lii J. H., Zhou T. S. Controlling the Chen attractor using linear feedback based on parameter identification [J]. Chin Phys, 2002, 11:12-16.
[74] Kocarev L, Parliza V. General approach for chaotic synchronization with application to commu- nication [J]. Physical Review Letters, 1995, 74:5028-5031.
[75] Matsumoto T., Chua L. O., Kobayashi K. Hyperchaos: laboratory experiment and numerical confirmation [J].IEEE Transactions on CAS, 1986, 33:1143-1147.
[76] Brucoli M., Carnimeo L., Grassi G.A method for the synchronization of hyperchaoticc ircuits[J].Int J Bifurcation and chaos, 1996,6:1673-1681.
[77] Grassi G, Mascolo.Nonlinear observer design to synchronize hyperchaotic systems via a scalar signal [J].IEEE Transactions on CAS-Ⅰ: Fundamental Theory and Applications,1997, 4:1011-1014.
[78] Wang T.B, Tan T.F. Coupled synchronization of hyperchaotic systems[J].Acta Physica Sinica,2001,50:1851-1855.
[79] Xiaofeng Liao, Zhongfu, and Juebang Yu, Hopf bifurcation analysis of a neural system with a continuously distributed delay[C], International Symposium on Signal Processing and Intelligent System, Guangzhou, China, 1999:546-549.
[80] Xiaofeng Liao, Zhongfu and Juebang Yu, Stability switches and bifurcation analysis of a neural network with continuously distributed delay [J].IEEE Trans. On SMC-Ⅰ, 1999, 29:692-696.
[81] K. Gopalsamy, I. Leung, Delay induced periodicity in a neural network of excitation and inhibition [J]. Physica D,1996, 89:395-426.
[82] 廖晓峰，吴中福，虞厥邦．带分布时延神经网络：从稳定到振荡再到稳定的动力学现象[J]．电子与信息学报，2001，23：689-692．
[83] Xiaofeng Liao, Kwok-wo Wong, Zhongfu Wu, Bifurcation analysis in a two-neuron system with continuously distributed delays. Physica D, 2001, 179:123-141.
[84] 靳藩编著．神经计算智能基础[M]．成都：西南交通大学出版社，2000．
[85] K. Murali, M. Lakshmanan, and L. O. Chua. The Simplest Dissipative Nonautonomous Chaotic Circuit [J]. IEEE Trans. on CAS-Ⅰ: Fundamental Theory and Applications. 1994, 41:462-463.
[86] Hongtao Lu, Yongbao He, and Zhenya He. A Chaos-Generator: Analyses of Complex Dynamics of a Cell Equation in Delayed Cellular Neural Networks [J]. IEEE Trans. on CAS-Ⅰ: Fundamental Theory and Applications. 1998, 45:178-181.
[87] Marco Gilli. Strange Attractors in Delayed Cellular Neural Networks [J]. IEEE Trans, on CAS-I:Fundamental Theory and Applications. 1993, 40:849-853.
[88] Hongtao Lu and Zhenya He. Chaotic Behavior in First-Order Autonomous Continuous-Time Systems with Delay [J]. IEEE Trans, on CAS-I: Fundamental Theory and Applications. 1996,43:699-702.
[89] K. Gopalsamy and Issic K. C. Leung. Convergence under Dynamical Thresholds with Delay [J].IEEE Trans, on Neural Networks. 1997, 8:341-348.
[90] J. Belair, S. Dufour. Stability in a three-dimensional system of delay-differential equations [J].Can. Appl. Math. Quart., 1996, 4:135-156.
[91] L. Olien, J. Belair, Bifurcations.Stability and monotonicity properties of a delayed neural network model [J], Physica D, 1997, 102:349-363.
[92] Aihara K, et al. Chaotic Neural Networks [J]. Phys. Lett. A, 1990, 144: 334-340.
[93] J. Belair, et. al., Frustration, Stability, and Delay-Induced Oscillations in a Neural Network Model [J]. SIAM Journal on Applied Mathematics, 1996, 56:245-255
[94] L.O. Chua, CNN: A Paradigm for Complexity [M]. World Scientific, Singapore, 1998.
[95] L.O. Chua, L. Yang, IEEE'Trans. Circuits Systems, 1988, 35:1273-1285.
[96] Nozawa H. A Neural - network Model as a Globally Coupled Map and Application Based on Chaos [J]. Chaos, 1992, 3:3140-3145.
[97] Inoue M, Nagayoshi A. A Chaos Neuro- computer [J ].Phys. Lett. A ., 1991 , 8 :373 - 76.
[98] R. J. Wang and W. J. Wang. Stability Analysis of Perturbed Systems with Multiple Noncommensurate Time Delays [J]. IEEE Trans. Circuits & Systems-I, 1996, 43:349-352.
[99] Y. J. Sun, et. al. On the Stability of Uncertain Systems with Multiple Time-Varying Delays [J].IEEE Transaction on Automatic Control, 1997, 42:101-105.
[100] H. S. Wu and K. Mizukami. New Sufficient Conditions for Robust Stability of Time-Delay Systems with Structured State Space Uncertainties[J].Transactions of the Society of Information Control Electronics, 1996, 32:336-344.
[101] J. Belair and S. A. Campell, Stability and Bifurcations of Equilibria in a Multiple-Delayed Differential Equation [J].SIAM J. Appl. Math., 1994, 54:1402-1424.
[102] S. A. Compell, et. al, Complex Dynamics and Multistability in a Damped Harmonic Oscillator with Delayed Negative Feedback[J].Chaos, 1995, 5:640-645.
[103] N. MacDonald, Harmonic Balance in Delay-Differential Equations [J].Journal of Sound and Vibration, 1995, 186:649-656.
[104] K. Sato et. al, Dynamic Motion of a Nonlinear Mechanical System with Time Delay (Analysis of the Self-Excited Vibration by an Averaging Method) [J], Transactions of Japanese Society of Mechanical Engineering, Series C, 1995, 61 :1855-1860.
[105] K. Sato et. al. Dynamic Motion of a Nonlinear Mechanical System with Time Delay (Analysis of the Forced Vibration by an Averaging Method) [J], Trans. JSME, Series C,1995,61:1861-1866.
[106] J. S. Lin and C. I. Weng.A Nonlinear Dynamic Model of Cutting [J].Int. J. Mach. Tools Manufact, 1990,30:53-64.
[107] Y. Tsuda, et. al., Chaotic Behavior of a Nonlinear Vibrating System with a Retarded Argument (Characteristics in the Region of Subharmonics Resonance) [J], Trans. JSME, Series C, 1993,59:2425-2432.
[108] E. Boe, H. C. Chang.Transition to Chaos from a two-torus in a delayed feedback system [J].Int.J. of Bifur. Chaos, 1991, 1:67-81.
[109] Y.Ueda, H.Ohta, H.B.Stewart.Bifurcation in a System Described by a Nonlinear Differential Equation with Delay [J], Chaos, 1994,4:75-83.
[110] K.Ikeda,K. Matsumoto.High-Dimensional Chaotic Behavior in Systems with Time-Delayed Feedback[J].Physica D, 1987, 29:223-235.
[111] S. Lepri, et.al, High-Dimensional Chaos in Delayed Dynamical Systems [J], Physica D, 1993,70:235-249.
[112] W. Just, et.al.Mechanism of Time-Delayed Feedback Control [J], Physical Review Letters, 1997, 78:203-206.
[113] P.Celka.Control of Time-Delayed Feedback Systems with Application to Optics [J],International Journal of Electronics, 1995, 79:787-795.
[114] J. E. S. Socolar, et.al., Stabilizing Unstable Periodic Orbits in Fast Dynamical Systems [J],Physics Reviews E, 1994, 50:3245-3248.
[115] K. Pyragas, Control of Chaos via Extended Delay Feedback [J], Phys. Lett. A, 1995,206:323-330.
[116] A. Kittle et.al. Delayed Feedback Control of Chaos by Self-Adapted Delay Time [J], Phys. Lett.A, 1995, 198:433-436.
[117] H. Nakajima, etal.Automatic Adjustment of Delay Time and Feedback Gain in Delayed Feedback Control of Chaos [J], IEICE Trans. Fundamentals, 1997, 9:1554-1559.
[118] Y. Tsuda, et. aL.On the Chaotic Behavior of Asymmetrical Duffing Oscillators [J], Trans. JSME,Series C, 1992,58:731-737.
[119] S. Boyd, L.EI. Ghaoui, E. Feron, V. Balakrishnan.Linear Matrix Inequalities in System and Control Theory [M]. SIAM, Philadelphia, PA, 1994.
[120] Skelton R. E., Iwasaki T. Increased roles of linear algebra in control education [J]. IEEE Control Syst. Mag., 1995, 15:76-89.
[121 ] Vandenberghe L ,Boyd S. Semidefinite programming [J]. SIAM Review, 1996, 38: 49-95.
[122] Balakrishnan V ,Feron E . Linear Matrix Inequalities in Control Theory and aplications [J].special issue of the Int. J. Robust and Nonlinear Control, 1996, 6: 896-1099.
[123] Balakrishnan V. ,Kashyap R L. Robust stability and performance analysis of uncertain systems using linear matrix inequalities [J]. J Optimization Theory and Applications, 1999, 100:457-478.
[124] Jeremy G. V., Braatz R. D. A tutorial on linear and bilinear matrix inequalities [J]. J. Process Control, 2000, 10:63-385.
[125] EI Ghaoui L , Niculescu S I. Advances in Matrix Inequality Methods in Control [M]. Advances in Design and Control. Philadelphia: SIAM, 2000.
[126] P. Gahinet, A. Nemirovskii, A.J. Laub, M. Chilali, LMI Control Toolbox User's Guide[M] The Math Works Inc., Natick, MA, 1995.
[127] Karmarkar N. K. A new polynomial-time algorithm for linear programming [J]. Combinatorica,1984, 4:373-395.
[128] Nesterov Y , Nemirovsky A. Interior-point polynomial methods in convex programming [M].Philadelphia: SIAM, 1994.
[129]Alizadeh F. Interior-point methods in semidefinite programming with applications to combinatorial optimization [J]. SIAM J. Optimization, 1995, 5: 13-51.
[130]T. Roska, L.O. Chua.Cellular neural networks with nonlinear and delay-type template [J].Int. J.Circuit Theory Appl., 1992, 20:469-481.
[131]C.M. Marcus, R.M, Westervelt.Stability of analog neural networks with delay [J]. Phys. Rev. A.,1989,39:347-359.
[132]M. Cohen, S. Grossberg.Absolute stability and global pattern formation and parallel memory storage by competitive neural networks [J]. IEEE Trans. Syst. Man Cybern, 1983, 13:815 - 826.
[133]P. van den Diressche, X. Zou, .Global attractivity in delayed Hopfield neural network models [J].SIAM J. Appl.Math., 1998, 58:1878 - 1890.
[134]J.D. Cao.Global exponential stability of Hopfield neural networks [J]. International Journal of Systems Science,2001,32:233 - 236.
[135]J.D. Cao, J. Wang. Absolute exponential stability of recurrent neural networks with Lipschitz-con tinuous activation functions and time delays[J].Neural Networks, 2004,17:379 - 390.
[136]H. Ye, A.N. Michel, K. Wang.Global stabilityand local stabilityof Hopfield neural networks with delays [J]. Phys. Rev. E, 1994, 50: 4206 - 4213.
[137]Y. Zhang, P.A. Heng, K.S. Leung.Convergence analysis of cellular neural networks with unbounded delay [J]. IEEE Trans. Circuits and Systems I, 2001, 48:680 - 687.
[138]Zou F, Nossek J.A.A chaotic attractor with cellular neural networks [J]. IEEE Trans. Circ. Syst. I,1991,38:811-812.
[139]Zou F, Nossek J.A.Bifurcation and chaos in cellular neural networks [J]. IEEE Trans. Circ. Syst. 1,1993,40:166-173.
[140]Gilli M.Strange attractors in delayed cellular neural networks[J].IEEE Trans.Circ.Syst.I,1993,40,:849-853.
[141]Lu H.T.Chaotic attractors in delayed neural networks [J].Phys. Lett. A, 2002,298:109 - 116.
[142]Lu H.T, He Z.Y.Chaotic behavior in first-order autonomous continuous-time systems with delay [J]. IEEE Trans. Circ. Syst. I, 1996,43:700 - 702.
[143]G.R. Chen, J. Zhou, Z.R. Liu.Global synchronization of coupled delayed neural networks and applications to chaotic CNN model [J].Int. J. Bifur. Chaos, 2004,14:2229 - 2240.
[144]C.W. Wu, L.O. Chua.Synchronization in an array of linearly coupled dynamical system [J].IEEE Trans. Circuit.Syst. I, 1995,42:430 - 447.
[145] W.L. Lu, T.P. Chen.Synchronization of coupled connected neural networks with delays [J]. IEEE Trans. Circuits. Syst. I, 2004,51:2491 - 2503.
[146]S. Mohamad, K. Gopalsamy.Exponential stability of continuous-time and discrete-time cellular neural networks with delays [J]. Appl. Math. Comput, 2003, 135:17-30.
[147]Q. Dong, K. Matsui, X. Huang.Existence and stability of periodic solutions for Hopfield neural network equations with periodic input[J] .Nonlinear Anal, 2002,49:471-479,.
[148]C.J. Cheng, T.L. Liao, C.C. Hwang, "Exponential synchronization of a class of chaotic neural networks," Chaos, Solitons and Fractals, 2005,24:197 - 206,.
[149] Gopalsamy K. Stability and oscillations in delay differential equations of population dynamics [M]. The Netherlands: Kluwer Academic Publishers, 1992.
[150] S.Xu, T.Chen, J.Lam.Robust H∞ filtering for uncertain Markovian jump systems with mode-dependent time delays[J ].IEEE Trans. Automat. Control, 2003,48 (5):900-907.
[151]Cao Jinde, Ho.Daniel W.C.A general framework for global asymptotic stability analysis of delayed neural networks based on LMI approach [J].Chaos Solitons and Fractals,2005,24 (5):1317-1329
[152] S.Boyd, L. E.Ghaoui, E.Feron, V.Balakrishnan. Linear Matrix Inequalities in System and Control Theory [M], SIAM, Philadelphia, PA, 1994.
[153] Halle K. S., Wu C.W. Spread spectrum communication through modulation of chaos in chua's circuit .Singapore: World scientific, 1993, 379-394
[154] 何思远等．混沌掩盖的同步通信技术[J]．沈阳航空工业学院学报，2005，22(5)：61-62．
[155] 张亚兵．混沌系统的同步及其在通信中的应用[D]．南京理工大学，2003．
[156] 蒋国平，王锁萍．细胞神经网络超混沌系统同步及其在保密通信中应用[J]．通信学报，2000，21(9)：79-85．