混沌系统的若干同步方法研究
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摘要
混沌是一种特殊复杂的非线性系统，普遍存在于自然界中。由于它的初值极端敏感性、高度随机性以及非线性方程的确定性，一直受到研究者的极大关注。混沌同步作为混沌科学的一个重要研究方向，自九十年代以来发展迅速，并在保密通信、图像处理等应用方面取得了可喜的进展。
本文基于非线性系统控制理论，研究了连续时间混沌系统、分段线性混沌系统的若干同步控制方法。论文的主要研究成果如下：
(1)提出了统一混沌系统的广义同步、脉冲时滞同步和SDRE同步三种方法
首先，提出了统一系统的广义同步方法。通过控制参数的不同选择，实现了状态完全同步和广义同步两种形式，该方法在保密通信中具有更高的安全性。然后，提出了统一系统的脉冲时滞反馈同步方法，同等脉冲信号强度下该方法加快了同步速度。最后，提出了统一系统的SDRE同步方法，具有给定稳定度的状态调节器改善了同步的动态性能。
(2)提出了含不确定参数的Liu混沌系统的自适应同步和变结构Backstepping同步两种方法
通过研究Liu混沌系统的单变量驱动和状态观测器两种同步方法，深入分析了Liu系统的结构特点。在此基础上，提出了自适应同步方法，设计了两种控制器，分别实现了线性项和非线性项不确定参数的辨识。然后，提出了变结构Backstepping同步方法，该方法系统性强，构造全局Lyapunov函数方便，成功实现了未知参数辨识和系统快速同步。
(3)为增强同步控制方法的通用性，提出了广义Lorenz系统的鲁棒H_∞模糊同步方法
广义Lorenz系统的鲁棒H_∞模糊同步方法在噪声干扰和系统参数不确定的情况下，仍具有较好的同步性能。该同步策略和控制模型适用于满足GLCF形式的一系列连续混沌系统。
(4)提出了异结构Liu-Genesio系统的Backstepping同步和超混沌Liu-R(?)ssler系统的Active同步方法
首先，提出了Liu混沌系统和Genesio混沌系统的Backstepping同步方法，设计了单一驱动和多驱动两种同步控制器，实现了Q-S同步形式，简化了控制器的结构。然后，提出了超混沌Liu系统和超混沌R(?)ssler系统的Active同步方法，并建立了状态完全同步、广义同步和滞后同步的统一控制模型。
(5)提出了一个新的分段线性混沌系统的基于LMI的反馈同步方法
在分析了新的分段线性混沌系统结构特点，研究了线性反馈和状态观测器两种同步方法的基础上，提出了一种基于LMI的反馈同步方法。转换后的分段混沌系统具有整体形式，只需利用LMI求取控制参量的可行解，避免了按分段函数讨论同步条件的麻烦，为一类分段混沌系统的同步控制研究提供了新思路。
最后总结分析了论文在混沌同步研究中的成果和不足，并指出了进一步的研究方向。
Chaos is a kind of special complicated nonlinear system, which is ubiquitous innature. Since it has the characteristics of sensitivity to initial values, high randomicityand certainty to nonlinear equations, chaos attracts great attentions from investigators.Chaotic synchronization is an important research aspect in chaotic science. Since1990, chaotic synchronization has achieved rapid development, its application insecure communications and image processing progress remarkably as well.
Based on control theories of nonlinear systems, this dissertation studies thesynchronization control methods of continuous-time and piecewise linear chaoticsystems. The main contributions are listed as follows:
(1) Three synchronization methods, including generalized synchronization,impulsive delay feedback synchronization and SDRE synchronization, are proposedfor unified chaotic system.
Firstly, the generalized synchronization method of unified system is proposed. Bychoosing different control parameters, the state completed synchronization (CS) andgeneralized synchronization (GS) of unified system are achieved. This method hashigher security in secure communications. Secondly, the impulsive delay feedbacksynchronization method is presented. It makes the synchronization speed quicker atthe same intensity of impulsive signals. Finally, the SDRE synchronization method ofunified system is brought forward. The state adjustors with given stability improve thesynchronization dynamic performance.
(2) Adaptive synchronization and variable structure Backstepping synchronizationmethods are proposed for Liu chaotic system with uncertain parameters.
After investigating the single variable driving synchronization and state observersynchronization methods, the structure characteristics of Liu chaotic system aredeeply analyzed. Based on it, the adaptive synchronization approach is presented.Two kinds of controllers are designed for identifying unknown linear or nonlinearparameters. Then the variable structure Backstepping synchronization method is putforward, which has strong systematization, easily constructs global Lyapunovfunctions and quickly realizes unknown parameters identification andsynchronization.
(3) To study the universal synchronization control method, the robust H_∞fuzzysynchronization method is proposed for generalized Lorenz systems.
With the noise disturbance and uncertain parameters, the robust H_∞fuzzy synchronization method for generalized Lorenz systems keep satisfiedsynchronization performance. The synchronization strategy and control models are fitfor all continuous chaotic systems which satisfy GLCF format.
(4) Backstepping synchronization and Active synchronization methods are proposedfor different structure chaotic systems: Liu-Genesio systems and hyperchaotic Liu-R(?)ssler systems.
Firstly, the Backstepping method is put forward to synchronize Liu system andGenesio system, which designs the single driving and multi-driving controllers aredesigned, receives Q-S synchronization format and simplifies the structures ofcontrollers. Secondly, the active synchronization method is presented for hyperchaoticLiu system and hyperchaotic R(?)ssler system. Moreover this method establishes theunified control models for completed synchronization, generalized synchronizationand delayed synchronization.
(5) Feedback synchronization method based on LMI is proposed for a new piecewiselinear chaotic system.
After analyzing the structure characteristics of the new piecewise linear chaoticsystem, studying linear feedback synchronization method and investigating stateobserver synchronization method, the feedback synchronization method based onLMI is proposed. The global format of transformed piecewise chaotic systems onlyneeds seek feasible solutions by LMI. So the method provides a new thought forsynchronizing a class piecewise chaotic systems.
Finally, some open issues on synchronization control of chaotic systems as wellas the future work are pointed out.
本文基于非线性系统控制理论，研究了连续时间混沌系统、分段线性混沌系统的若干同步控制方法。论文的主要研究成果如下：
(1)提出了统一混沌系统的广义同步、脉冲时滞同步和SDRE同步三种方法
首先，提出了统一系统的广义同步方法。通过控制参数的不同选择，实现了状态完全同步和广义同步两种形式，该方法在保密通信中具有更高的安全性。然后，提出了统一系统的脉冲时滞反馈同步方法，同等脉冲信号强度下该方法加快了同步速度。最后，提出了统一系统的SDRE同步方法，具有给定稳定度的状态调节器改善了同步的动态性能。
(2)提出了含不确定参数的Liu混沌系统的自适应同步和变结构Backstepping同步两种方法
通过研究Liu混沌系统的单变量驱动和状态观测器两种同步方法，深入分析了Liu系统的结构特点。在此基础上，提出了自适应同步方法，设计了两种控制器，分别实现了线性项和非线性项不确定参数的辨识。然后，提出了变结构Backstepping同步方法，该方法系统性强，构造全局Lyapunov函数方便，成功实现了未知参数辨识和系统快速同步。
(3)为增强同步控制方法的通用性，提出了广义Lorenz系统的鲁棒H_∞模糊同步方法
广义Lorenz系统的鲁棒H_∞模糊同步方法在噪声干扰和系统参数不确定的情况下，仍具有较好的同步性能。该同步策略和控制模型适用于满足GLCF形式的一系列连续混沌系统。
(4)提出了异结构Liu-Genesio系统的Backstepping同步和超混沌Liu-R(?)ssler系统的Active同步方法
首先，提出了Liu混沌系统和Genesio混沌系统的Backstepping同步方法，设计了单一驱动和多驱动两种同步控制器，实现了Q-S同步形式，简化了控制器的结构。然后，提出了超混沌Liu系统和超混沌R(?)ssler系统的Active同步方法，并建立了状态完全同步、广义同步和滞后同步的统一控制模型。
(5)提出了一个新的分段线性混沌系统的基于LMI的反馈同步方法
在分析了新的分段线性混沌系统结构特点，研究了线性反馈和状态观测器两种同步方法的基础上，提出了一种基于LMI的反馈同步方法。转换后的分段混沌系统具有整体形式，只需利用LMI求取控制参量的可行解，避免了按分段函数讨论同步条件的麻烦，为一类分段混沌系统的同步控制研究提供了新思路。
最后总结分析了论文在混沌同步研究中的成果和不足，并指出了进一步的研究方向。
Chaos is a kind of special complicated nonlinear system, which is ubiquitous innature. Since it has the characteristics of sensitivity to initial values, high randomicityand certainty to nonlinear equations, chaos attracts great attentions from investigators.Chaotic synchronization is an important research aspect in chaotic science. Since1990, chaotic synchronization has achieved rapid development, its application insecure communications and image processing progress remarkably as well.
Based on control theories of nonlinear systems, this dissertation studies thesynchronization control methods of continuous-time and piecewise linear chaoticsystems. The main contributions are listed as follows:
(1) Three synchronization methods, including generalized synchronization,impulsive delay feedback synchronization and SDRE synchronization, are proposedfor unified chaotic system.
Firstly, the generalized synchronization method of unified system is proposed. Bychoosing different control parameters, the state completed synchronization (CS) andgeneralized synchronization (GS) of unified system are achieved. This method hashigher security in secure communications. Secondly, the impulsive delay feedbacksynchronization method is presented. It makes the synchronization speed quicker atthe same intensity of impulsive signals. Finally, the SDRE synchronization method ofunified system is brought forward. The state adjustors with given stability improve thesynchronization dynamic performance.
(2) Adaptive synchronization and variable structure Backstepping synchronizationmethods are proposed for Liu chaotic system with uncertain parameters.
After investigating the single variable driving synchronization and state observersynchronization methods, the structure characteristics of Liu chaotic system aredeeply analyzed. Based on it, the adaptive synchronization approach is presented.Two kinds of controllers are designed for identifying unknown linear or nonlinearparameters. Then the variable structure Backstepping synchronization method is putforward, which has strong systematization, easily constructs global Lyapunovfunctions and quickly realizes unknown parameters identification andsynchronization.
(3) To study the universal synchronization control method, the robust H_∞fuzzysynchronization method is proposed for generalized Lorenz systems.
With the noise disturbance and uncertain parameters, the robust H_∞fuzzy synchronization method for generalized Lorenz systems keep satisfiedsynchronization performance. The synchronization strategy and control models are fitfor all continuous chaotic systems which satisfy GLCF format.
(4) Backstepping synchronization and Active synchronization methods are proposedfor different structure chaotic systems: Liu-Genesio systems and hyperchaotic Liu-R(?)ssler systems.
Firstly, the Backstepping method is put forward to synchronize Liu system andGenesio system, which designs the single driving and multi-driving controllers aredesigned, receives Q-S synchronization format and simplifies the structures ofcontrollers. Secondly, the active synchronization method is presented for hyperchaoticLiu system and hyperchaotic R(?)ssler system. Moreover this method establishes theunified control models for completed synchronization, generalized synchronizationand delayed synchronization.
(5) Feedback synchronization method based on LMI is proposed for a new piecewiselinear chaotic system.
After analyzing the structure characteristics of the new piecewise linear chaoticsystem, studying linear feedback synchronization method and investigating stateobserver synchronization method, the feedback synchronization method based onLMI is proposed. The global format of transformed piecewise chaotic systems onlyneeds seek feasible solutions by LMI. So the method provides a new thought forsynchronizing a class piecewise chaotic systems.
Finally, some open issues on synchronization control of chaotic systems as wellas the future work are pointed out.
引文
[1] Hao B.L. Chaos. Singapore: World Scientific, 1984
[2] Hao B.L. Chaos Ⅱ. Singapore: World Scientific, 1990
[3] Lorenz E.N. Deterministic non-periodic flow. J. Atmos. Sci. 1963, 20:130-141
[4] Sivakumar B. Chaos theory in geophysics: past, present and future. Chaos, Solitons & Fractals, 2004, 19(2): 441-462
[5] Feigenbaum M,J. Quantitalive university for a class of nonlinear transformation. J. Star. Phys. 1978, 19:25-28
[6] Freeman W.H., Mandebort B.B. Fractal, form, chance and dimension. San Francisco, 1977
[7] Fleming W.H. Future directions in control theory: a mathematical perspective. SIAM Pub., 1988, 50-51
[8] Chen G.R., Dong X. From chaos to order: methodologies, perspectives and applications. Singapore: World Scientific, 1998
[9] Rossler O.E. An equation for continuous chaos. Physical Letters A, 1976, 57:397-398
[10] Chua L.O., Komuro M., Matsumoto T. The double scroll family. Part Ⅰ: rigorous proof of chaos. IEEE Trans. on Circuits & Systems-Ⅰ, 1986, 33: 1072-1096
[11] Chen G.R., Ueta T. Yet another chaotic attractor. Int. J. Bifurcation & Chaos, 1999, 9: 1465-1466
[12] Lu J.H., Chen G.R., Cheng D.Z. Bridge the gap between the Lorenz system and the Chen system. Int. J. Bifurcation & Chaos, 2002, 12(12): 2917-2926
[13] Lu J.H., Chen G.R., Yu X. Dynamical behaviors of a unified chaotic system, Dynamical of continuous, Discrete and Impulsive Systems Series B, 2003, Sup: 115-124
[14] Liu C.X,, Liu T., Liu L. A new chaotic attractor. Chaos, Solitons & Fractals, 2004, 22: 1031-1038
[15] Liu C.X., Liu L., Liu T. A new butterfly-shaped attractor of Lorenz-like system. Chaos, Solitons & Fractals, 2006, 28:1196-1203
[16] Wang F. Q., Liu C.X. Hyperchaos evolved from the Liu chaotic system. Chinese Physics, 2006, 15(5): 963-968
[17] Vanecek A., Celikovsky S. Control systems: From linear analysis to synthesis of chaos. London: Prentice Hall, 1996
[18] Lu J.H., Zhou T.S., Chen G.R., et al. Generating chaos with a switching piecewise-linear controller. Chaos, 2002, 12(2): 344-349
[19] Zheng Z.H., Lu J.H., Chen G.R., et al. Generating two simultaneously chaotic attractors with a switching piecewise-linear controller. Chaos, Solitons & Fractals, 2004, 20:277-288
[20] Li T.Y., Yorke J.A. Period three implies chaos. Amer. Math. Monthly, 1975, 82:985-992
[21] 关新平，范正平，陈彩莲．混沌控制及其在保密通信中的应用．北京：国防工业出版社，1993
[22] 方锦清，赵耿，罗晓曙．混沌保密通信应用研究的进展．广西师范大学学报(自然科学版)，2002，20(1)：6-18
[23] Windell H.O. Atom optics experiments in quantum chaos: [Doctor Degree Dissertation], USA, The University of Texas, 2001
[24] Gong J.B. Coherent control, quantum chaos, and decoherence in molecula: [Doctor Degree Dissertationl, Canada, University of Toronto, 2001
[25] 王光瑞，于煦龄，陈式刚．混沌的控制、同步和利用．北京：国防工业出版社，2001
[26] 邹恩，李详飞，陈建国等著．混沌控制及其优化应用．长沙：国防科技大学出版社，2002
[27] Iasonas K., Petros M. Nonlinear speech analysis using models for chaotic systems. IEEE Trans. on Speech & Audio Processing, 2005, 13(6): 1098-1109
[28] Feng J.C., Tse C.K., Francis C.M. A neural-network-based channel-equalization strategy for chaos-based communication systems. IEEE Trans. on Circuits & System-I, 2003, 50(7): 954-957
[29] Alexander L.B., Wolfgang S. Chaotic and random point processes: analysis, design, and applications to switching systems. IEEE Trans. on Circuits & System-I, 2003, 50(8): 1081-1088
[30] 覃团发，唐秋玲，姚海涛．实时数字语音混沌保密通信系统．计算技术与自动化，2000，19(1)：58-61
[31] 李昌刚，韩正之．一种基于离散混沌系统的密钥流设计算法，信息与控制，2002，31(5)：407-411
[32] Chen L., Aihara K. Global search ability of chaotic neural networks. IEEE Trans. on Circuits & Systems-I, 1999, 46(8): 974-993
[33] Ma W., Wang Z.O. A new chaotic parameters annealing neural network for solving global optimization problems. Comlnun. Theor. Phys., 2003, 39(4): 385-392
[34] 骆晨钟，邵惠鹤．用混沌搜索求解非线性约束优化问题．系统工程理论与实践，2002，8：54-57
[35] 李兵，蒋慰孙．混沌优化方法及其应用．控制理论与应用，1997，14(4)：613-615
[36] 孟红记，郑鹏，梅国晖．基于混沌序列的粒子群优化算法．控制与决策，2005，21(3)：263-266
[37] 张彤，王宏伟，王子才．变尺度混沌优化方法及其应用．控制与决策，1999，14(3)：285-288
[38] Sabri A. Global asymptotic stability of a class of dynamical neural networks. IEEE Trans. on Circuits & Systems-I, 2000, 47(4): 568-571
[39] Qiu S.S. A cell model of chaotic attractor. Proceedings IEEE ISCAS'97, HongKong, 1997
[40] 王凌，郑大钟．一种基于退火策略的混沌神经网络优化算法．控制理论与应用，2000，17(1)：139-142
[41] 陈冬，戴琼海，徐文立，引入混沌机制处理HFC网络回传噪声问题．清华大学学报(自然科学版)，2002，42(11)：1556-1559
[42] 蒋传文，权先璋，李承军，张勇传．混沌理论在电力负荷预测中的应用，武汉交通科技大学学报，1999，23(61：609-612
[43] 薛禹胜，周海强，顾晓荣．电力系统分岔与混沌研究述评，电子系统自动化，2002，26(16)：9-15
[44] 张波，李忠，毛宗源．永磁同步电动机的混沌特性及其反混沌控制．控制理论与应用，2002，19(4)：545-548
[45] Ott E., Grebogi C., Yorke J.A. Controlling chaos, Physical Review Letters, 1990, 64(11): 1196-1199
[46] Gallego J.A. Nonlinear regulation of a Lorenz system by feedback linearization techniques. Dynamic Control, 1994, 4:277-298
[47] Chen G.R., Dong X. On feedback control of chaotic continuous-time systems. IEEE Trans. on Circuits & Systems, 1993, 40(9): 591-601
[48] Chen G.R., Dong X. Controlling Chua's system. J. Circuits, Systems & Computations, 1993, 3:139-148
[49] Naumenko A.V., loiko N.A., Turovets S.I. Chaos control in external cavity laser diodes using electroni impulsive delayed feedback. Int. J. Bifuracation & Chaos, 1996, 6:1791-1799
[50] 李伟，陈式刚．用周期拍方法控制非线性耗散系统和保守系统的混沌，物理学报，2001，50(10)：1862-1870
[51] Yu Y.G., Zhang S.C. Adaptive backstepping control of the uncertain Lu system. Chinese Physics, 2002, 12(11): 1249-1253
[52] 张思进，陆启韶，王士敏．碰摩转子映射系统的延迟反馈混沌控制．固体力学学报，2001，22(3)：89-94
[53] Chen L. Predictive fuzzy control of uncertain chaotic systems: [Doctor degree dissertation], USA, University of Houston, 1998
[54] Li Z, Han C.Z. Adaptive control and identification of chaotic systems. Chinese Physics, 2001, 10(6):494-496
[55] 李智，韩祟昭．一类含参数不确定性混沌系统的自适应控制，物理学报，2001，50(5)：847-850
[56] 王中生，何汉林，廖晓昕．含多参数的不确定线性时滞系统的鲁棒镇定．华中科技大学学报，2003，31(5)：36-38
[57] 张毅锋，何振亚，杨绿溪．用脉冲控制法抑制非自治细胞神经网络中的混沌．控制与决策，1999，14(5)：418-422
[58] 罗晓曙．非线性系统中的混沌控制与同步及其应用研究：[博士学位论文]，北京：中国科学技术大学，2003
[59] Luo X.S., Wang B.H., Jiang F. Using random proportional pulse feedback of system variables to control chaos and hyperchaos. Chinese Physics, 2001, 10(1): 17-20
[60] Luo X.S., Fang J.Q. A method of controlling spatiotemporal chaos in coupled map lattices. Chinese Physics, 2000, 9(5): 333-336
[61] 薛月菊，冯汝鹏．连续时间耦合系统中时空混沌的自适应模糊控制．物理学报，2001，50(3)：440-444
[62] 方天华．超混沌同步的非线性控制法．原子能科学技术，1998，32(2)：184-187
[63] Vincent T.L., Yu J. Control of a chaotic System. Dynamic Control, 1991, 1:35-52
[64] Zhang Y., Wen C., Sob Y.C. Discrete-time robust backstepping adaptive control for nonlinear time-varying systems. IEEE Trans. on Automatic Control, 2000, 45:1749-1755
[65] Lu J.H, Lu J.A. Controlling uncertain Lu system using linear feedback. Chaos, Soliton & Fractals, 2003, 17(1): 127-133
[66] Lu J.H, Zhou T., Zhang S. Controlling Chen system using feedback function based on parameters identification. Chinese Physics, 2002, 12(10): 2257-2270
[67] 吴忠强，赵海英．一种模糊滑模变结构控制方案及其在混沌系统控制中的应用．信息与控制，2002，31(3)：280-283
[68] Gohary A.E., Yassen R. Adaptive control and synchronization of a conpled dynamo system with uncertain parameters. Chaos, Solitons & Fractals, 2006, 29:1085-1094
[69] Zou Y.L., Zhu J. Controlling the chaotic n-scroll Chua's c(?)cuit with two low-pass filters. Chaos, Solitons & Fractals, 2006, 29:400-406
[70] Barbara C., Silvano C., Alessandro P.Controlling chaos via second-order sliding modes. ISCAS 2003．Ⅲ：156-159
[71] 张晓辉，沈柯．高周期混沌轨道的构造方法和应用，物理学报，1999，48(12)：2186-2190
[72] Yang L., Liu Z. R. and Mao J. Controlling hyperchaos, Physical Review Letters, 2004, 84: 67
[73] Guan X. P., Hua C. C., Duan G. R. Comments on "Robust stabilization of a class of time-delay nonlinear systems". IEEE Trans. on Automatic Control, 2003, 48(5): 907-908
[74] Liu G. G., Zhao Y. Adaptive control on a class of uncertain chaotic systems. Chinese Physical Letters, 2005, 22(5): 1069-1071
[75] Tsui A. P., Jones A. J. The control of higher dimensional chaos: comparative results for the chaotic satellite attitude control problem. Physica D, 2000, 135: 41-62
[76] Lu J. A., Xie J., Lu J. H. Control chaos in transition system using sampled-data feedback. Applied Methematics & Mechanics, 2003, 24(11): 1309-1316
[77] Yu H. J., Lin Y. Z., Peng J. H. Continuous control of chaos based on the stability criterion. Physical Review E, 2004, 69(62): 066203
[78] Wang Z. S., Liao X. X. Adaptive synchronization and parameter identification for a unified chaotic system. 2004 Int. Conf. Information Acquisition, 2004: 20-22
[79] Yu D. C., Wu A. G., Wang D. Q. A simple asymptotic trajectory control of full sates of a unified chaotic system. Chinese Physics, 2006, 15(2): 306-309
[80] 修春波，刘向东，张宇河．混沌优化与模糊控制在混沌控制中的应用．控制理论与应用，2005，22(1)：63-67
[81] Pecora L. M., Carroll T. L. Synchronization in chaotic systems. Physical Review Letters, 1990, 64(8): 821-825
[82] Chert G. R., Lai D. Feedback control of Lyapunov exponents for dynamic systems. Int. J. Bifurcation & Chaos, 1996, 6: 1341-1349
[83] Wang X. F., Chen G. R. Chaotifying a stable LTI system by tiny feedback control. IEEE Trans. on Circuits & Systems, 2000, 47: 410-415
[84] Wang X. F., Chen G. R. Chaotifying a stable map via smooth small-amplitude high-frequency feedback control. Int. J. Circuit Theory & Application, 2000, 28: 305-312
[85] Wang X. F., Chen G. R., Yu X. Anticontrol of chaos in continuous-time systems via time-delay feedback. Chaos, 2000, 1: 771-779
[86] 卢俊国．混沌同步与反控制的若干问题研究：[博士后工作报告]，上海：上海交通大学，2003
[87] 甘春标，郭乙木．拟可积哈密顿系统中噪声诱发的混沌运动，力学学报，2000，32(5)：613-620
[88] Tang K. S., Man K.E, Zhong G. Q. Generating chaos via x|x|. IEEE Trans. on Circuits & Systems-Ⅰ: 2001, 48(5): 636-641
[89] Li Y. X., Chen G. R., Wallace K. S. Controlling a unified chaotic system to hyperchaotic. IEEE Trans. on Circuit & Systems-H, 2005, 52(4): 204-207
[90] Codreanu S. Desynchronization and chaotification of nonlinear dynamical systems. Chaos, Solitons & Fractals, 2002, 13: 839-843
[91] Potapov A., Ali M. K. Chaotic Neural Control. Physical Review E63: 046215
[92] Sanchez E. N., Perez J. P., Chert G. R. Using dynamic neural network to generate chaos: an inverse optimal control approach. Int. J. Bifurcation & Chaos, 2001, 11: 857-863
[93] Chen G. R., Yang L., Liu Z. R. Anticontrol of chaos for continuous-time systems. IEICE Trans. on Fundamentals of Electronics, Communications and Computer Sciences, 2002, E85A(6): 1333-1335
[94] 张丽丽，张晓丹．四维线性微分系统的混沌反控制理论及应用．北京科技大学学报，2004，26(6)：673-677
[95] 朱淑芹，杨淼，张先华，闵乐泉．利用Silnikov定理构造混沌系统．北京科技大学学报，2005，27(5)：636-638
[96] Salama K.N., Ozoguz S., Elwakil A.S. Generation of n-scroll chaos using nonlinear transconductors. ISCAS 2003, Ⅲ: 176-179
[97] Wallace K.S., Tang G.Q., Chen Z.G. Generation of n-scroll attractors via sine function. IEEE Trans. on Circuits & Systems-I: 2001, 48(11): 1369-1372
[98] Wang J.Z., Chen Z.Q., Yuan Z.Z. The generation of a hyperchaotic system based on a three-dimensional autonomous chaotic system. Chinese Physics, 2006, 15(6): 1216-1225
[99] Li X., Chert Z.Q., Yuan Z.Z. Generating Chaos by an Elman Network. IEEE Trans. on Circuits & systems-I, 2001, 48(11): 1126-1131
[100] Lin W., Ruan J., Zhao W.R. On the mathematical clarification of the snap-back-repeller in high-dimensional system and chaos in a discrete neural network model. Int. J. Bifurcation & Chaos, 2002, 12(5): 1129-1139
[101] 王兴元，杨威，边丽英．构造广义Rossler奇怪吸引子的一种新方法，东北大学学报(自然科学版)，2001，22(3)：261-264
[102] Liu Z.R., Chung K.W. Hybrid control of bifurcation in continuous nonlinear dynamical systems. Int. J. of Bifurcation and Chaos, 2005, 15(I2): 3895-3903
[103] Radoslav R., Elena V., Chen G.R. Local bang-bang control of a chaotic system with two 2-scroll attractors. Dynamic of Continuous Discrete and Impulsive Systems Series B, 2004, 11a: 152-158
[104] Lu J.A., Tao C.H. Parameter identification and tracking of a unified system. Chinese Physical Letters, 2002, 19 (5): 632-635
[105] 关新平，范正平，龙承念．非线性不确定时滞混沌系统的鲁棒控制．控制理论与应用，2002，19(2)：211-214
[106] Kuang Y.L., Liu P., Wei C.L. Robust chaotic fuzzy output tracking control. IEEE Int. Fuzzy Systems Conference, 2001: 1577-1580
[107] Lewis C.T. Issues in chaos synchronization: subhannonic destruction, multi-valued mappings, and chaotic lightwave communication: [Doctor degree dissertation], USA, University of California, 2001
[108] Li X.J., Zhang Y., Du G.H. An investigation on chaotic behavior of two forms of ray eouations, J. of Nanjing University (Natural Sciences), 2000, 36(3): 383-386
[109] 文成秀，赵长宽，闻邦椿．分段线性振动机械关于外激振频率的分岔与混沌，东北大学学报(自然科学版)，2001，22(2)：200-202
[110] 戴栋，马西奎，李小峰．一类具有两个边界的分段光滑系统中边界碰撞分岔现象及混沌，物理学报，2003，52(11)：2729-2736
[111] Brown R., Kocarev L. A unifying definition of synchronization for dynamical systems. Chaos, 2000, 10(2): 344-349
[112] Yan Z.Y. Q-S(lag or anticipated) synchronization backstepping scheme in a class of continuous-time hyperchaotic system. Chaos, 2005, 15:023902
[113] Yah Z.Y. Chaos Q-S synchronization between Rossler system and the new unified chaotic system. Physical Letters A, 2005, 334:406
[114] 陶朝海，陆君安，吕金虎．统一混沌系统的反馈同步．物理学报，2002，51(7)：1497-1501
[115] Lu J.G. Chaotic dynamics and synchronization of fractional-order Arneodo's systems. Chaos, Solitons & Fractals, 2005, 26(4): 1125-1133
[116] 王福田，洪奕光．关于混沌系统的鲁棒和自适应同步化．控制理论与应用，2000，17(3)：55-59
[117] Alexander E.H., Alexey A.K. An approach to chaotic synchronization. Chaos, 14(3): 603-610
[118] Li Y.N., Chen L. Cai Z.S. Chaos synchronization in the Belousov-Zhabotinsky reaction by adaptive control scheme. Chinese Journal of Chemistry, 2002, 20:753-759
[119] Liu W.B., Chen G.R. Control and synchronization of a 4-scroll chaotic system. ISCAS 2003, Ⅲ: 100-103
[120] Li F., Hu A.H. Xu Z.Y. Robust synchronization of uncertain chaotic systems. Chinese Physics, 2006, 15(3): 507-512
[121] Williams C. A robust chaotic communications system based on generalized synchronization. 1998 IEEE Int. Conf. on Electronics, Circuits and Systems, 1998:243-246
[122] Wang Y.W., Guan Z.H. Generalized synchronization of continuous chaotic system. Chaos, Solitons & Fractals, 2006, 27(1): 97-101
[123] Shahverdiev E.M., Sivaprakasam S., Shore K.A. Lag synchronization in time delayed system. Physical Review A, 2002, 292(6): 320-324
[124] Taherion S., Lai Y.C. Observability of lag synchronization of coupled chaotic oscillators. Physical Review E, 1999, 59(6): 6247-6250
[125] Chen J.Y., Wong K.W. Phase synchronizationin discrete chaotic systems. Physical Review E, 2000, 61(3): 2559-2562
[126] 桑海波，贺凯芬．用外加周期信号控制时空混沌中的相同步．北京师范大学学报(自然科学版)，2004，40(3)：350-353
[127] Yan Z.Y. Q-S synchronization in 3D Henon-like map and generalized Henon map via a scalar controller. Physics Letters A, 2005, 342:309-317
[128] 程丽，张入元，彭建华．用单一驱动变量同步混沌与超混沌的一种方法．物理学报，2003，52(3)：536-541
[129] Kocarev L., Parlitz U. General approach for chaotic synchronization with applications to communication. Physical Review Letters, 1995, 74: 5028-5031
[130] Surkens J.A., Curren P E., Chua L.O. Robust synthesis for master-slave synchronization of Lur'e systems. IEEE Trans. on Circuits & Systems-I, 1999, 46(7):841-850
[131] 罗晓曙，方锦清．用离散混沌信号驱动实现混沌同步．物理学报，1999，48(11)：2022-2028
[132] Wang R., Shen K. Synchronization of chaotic erbium-doped fiber dual-ring lasers by using the method of another chaotic system to drive them. Physical Review E, 2002, 65(1): 016207
[133] 赖建文，周世平，李国辉，等．间歇驱动混沌同步法．物理学报，2001，50(1)：21-25
[134] 肖宏芳，黄祖达．半线性驱动-响应系统在输出反馈控制下的混沌同步．数学理论与应用，2005，25(4)：72-74
[135] Stojanovski T., Kocarev L., Parlitz U. Spiradic driving of dynamical systems. Physical Review E, 1997, 55(4): 4035-4047
[136] Kocarev L., Parlitz U., Stojanovski T. Chaos synchronization using sporadic driving. Physical D, 1997, 109:139-152
[137] 杨世平，牛海燕，田钢，等．用驱动参量法实现混沌系统的同步．物理学报，2001，50(4)：619-623
[138] Pyragas K. Continous control of chaos by self-controlling systems. Physical Letters A, 1992, 170:421-428
[139] Pyragas K., Tamasevicius A. Experimental control of chaos by delayed selfcontrolling feedback. Physical Letters A, 1993,180: 99-102
[140] 唐芳，邱琦．混沌系统的辅助参考反馈控制．物理学报，1999，48(5)：802-807
[141] Jiang G.P., Tang K.S. A global synchronization criterion for coupled chaotic systems via unidirectional linear error feedback approach. Int. J. Bifurcation Chaos, 2002, 12(10): 2239-2253
[142] Bu S.L., Wang S.Q., Ye H.Q. An algorithm based on variable feedback to synchronize chaotic and hyperchaotic systems. Physica D, 2002, 164:45-52
[143] 高金峰，罗先觉，马西奎．控制与同步连续时间混沌系统的非线性反馈方法，物理学报，1999，48(9)：1618-1627
[144] 刘扬正，费树岷．Genesio-Tesi和Coullet混沌系统之间的非线性反馈同步．物理学报，2005，54(8)：3486-3490
[145] 陶朝海，陆君安．混沌系统的速度反馈同步．物理学报，2005，54(11)：5058-5061
[146] Hang F. L. Yu X.H., Feng Y. A further study of nonlinear feedback system with chaotic oscillation. WCICA 2004-Fifth World Congress on Intelligent Control and Automation, 2004: 83-86.
[147] Roy R. Experimental synchronization of chaos. Physical Review Letters, 1994, 72(13): 2009-2012
[148] Sugawara T. Observation of synchronization in laser chaos. Physical Review Letters, 1994, 72(22): 3502-3505
[149] Kapitaniak T. Experimental synchronization of chaos using continuous control. Int. J. Bifirurcation & Chaos, 1994, 4(2): 483-488
[150] Angeli A.D., Chua L.O. Dead-Beat chaos synchronization in discrete-time systems. IEEE Trans. on Circuits & Systems, 1995, 2(1): 54-56
[151] Wn C,W., Chua L.O. Synchronization in and array of linearly coupled dynamical systems. IEEE Trans. on Circuits & Systems-I, 1995, 42(8): 430-447
[152] 蒋品群，汪秉宏，罗晓曙．四阶蔡氏超混沌电路的单向耦合同步研究．系统工程与电子技术，2004，25(9)：119-1121
[153] 张旭，沈柯．时空混沌的单向耦合同步，物理学报，2002，51(12)：2702-2706
[154] Lu J.H., Zhou T.S., Zhang S.C. Chaos synchronization between linearly coupled chaotic systems. Chaos, Solitons & Fractals, 2002, 14:529-541
[155] Li D.M., Lu J.A., Wu X.Q. Linearly coupled synchronization of the unified chaotic systems and the Lorenz systems. Chaos, solitons & Fractals, 2005, 23:79-85
[156] Ju H.P. Stability criterion for synchronization of linearly coupled unified chaotic systems, Chaos, Solitons & Fractals, 2005, 23:1319-1325
[157] 闵富红，王执铨．统一混沌系统的耦合同步．物理学报，2005，54(9)：4026-4030
[158] 卢俊国，汪小帆，王执铨．连续时间混沌系统控制与同步的状态反馈方法．控制与决策， 2001，16(4)：476—479
[159] 张宇，余俊明，杜功焕．连续反馈混沌同步方式在保密通讯的中应用．科学通报，1998，43(17)：1831-1835
[160] Bai E.W., Lonngren K.E. Sequential synchronization of two Lorenz systems using active control. Chaos, Solitons & Fractals, 2000, 11: 1041-1044
[161] Kouomou Y.C., Woafo P. Stability and optimization of chaos synchronization through feedback coupling with delay. Physics Letters A, 2002, 298:18-28
[162] 戴旭初，张锦钢，徐佩霞．一种基于耦合反馈的离散组合混沌系统的同步方法．控制理论与应用，2000，17(5)：789-792
[163] Morgul O., Solak E. On the synchronization of chaotic systems by using state observations. Int. J. Bifurcation & Chaos, 1997, 7(6): 1307-1322
[164] Nijmeijer H., Mareeis I.M. An Observer Looks at Synchronization. IEEE Trans. on Circuits & Systems-I, 1997, 44(10): 882-890
[165] 李世华，蔡海兴．Chen氏混沌电路实现与同步控制实验研究．物理学报，2004，53(6)：1687-1693
[166] 张学义，李殿璞，陈实如．基于状态观测器超混沌系统高精度保密通信方法．电路与系统学报，2001，6(4)：5-18
[167] 杨涛，邵惠鹤．一类混沌系统的同步方法．物理学报，2002，51(4)：742-748
[168] Boutayeb M., Darouach M., Rafaralyahy H. Generalized state-space observers for chaotic synchronization and secure commtmication. IEEE. Trans. Circuits & Systems-I, 2002, 49(3): 345-349
[169] Wang W.W., Gao Z.Q. A comparison study of advanced state observer design teclmiques. Proceedings of the American Control Conference, Colorado, 2003, June 4-6
[170] 姚利娜，高金峰，廖旎焕．实现混沌系统同步的非线性状态观测器方法．物理学报，2006，55(1)：35-41
[171] Li G.H., Zhou S.P., Xu D.M. Chaos synchronization based on intermittent state observer. Chinese Physics, 2004, 13(2): 168-172
[172] Jolly K.J., Amritkar R.E. Synchronization of unstable orbits using adaptive control. Physical Review E, 1994, 94:4883
[173] Fradkov A.L., Pogromsky Y.A. Speed gradient control of chaotic continuous-time systems. IEEE Trans. on Circuits & Systems-I: 1996, 43(11): 907-913
[174] Andrievsky B. Adaptive synchronization methods for signal transmission on chaotic carriers. Mathematics and Computers in Simulation, 2002, 58:289-293
[175] Liao T.L., Tsai S.H. Adaptive synchronization of chaotic systems and its application to secure communications. Chaos, Solitons & Fractals, 2000, 11:1387-1396
[176] Femat R., Alvarez R.J., Fernendez A.G. Adaptive synchronization of high-order chaotic systems: a feedback with low-order parametrization. Physica D, 2000, 139:231-246
[177] 齐冬莲，魏金岭，赵光宙．基于系统辨识的自适应混沌同步控制研究，控制与决策，2001，16(5)：120-122
[178] Wang C., Ge S.S. Adaptive synchronization of uncertain chaotic systems via backstepping design. Chaos Solitons & Fractals, 2001, 12:1119-1206
[179] Dai D., Ma X.K. Chaos synchronization by using intermittent parametric adaptive control method. Physics Letters A, 2001, 288:23-28
[180] 关新平，陈彩莲，范正平．基于backstepping方法的混沌系统自适应模糊控制．物理学报，2002，51(4)：753-758
[181] 范正平．混沌控制、同步及在保密通信中的应用：[博士学位论文]，河北：燕山大学，2003
[182] Wang Z. L., Zhang H. G. Adaptive synchronization of discrete chaotic systems, Proceedings of 2002 Int. Conf. on Machine Learning and Cybernetics, 2002: 336-339
[183] 樊春霞，姜长生．统一混沌系统自适应同步控制．系统工程与电子技术，2004，26(3)：358-360
[184] 孙克辉，陈志盛，张泰山．基于参数自适应方法的统一混沌系统的同步控制．信息与控制，2005，34(1)：40-43
[185] Wang Y. W., Guan Z. H. Adaptive synchronization for Chen chaotic system with fully unknown parameters. Chaos, Solitons & Fractals, 2004, 19(4): 899-903
[186] Wang Z. S., Liao X. X. Synchronization and parameters identification of chaotic systems via adaptive control. J. of Electronic Science and Technology of China, 2005, 3(1): 64-67
[187] 刘国刚，赵怡．参数不确定混沌系统的自适应同步控制，电路与系统学报，2005，10(1)：24-27
[188] 王兴元，武相军．不确定Chen系统的参数辨识与自适应同步，物理学报，2006，55(2)：605-609
[189] Kuang Y. L., Peter L., Tung S. C. Adaptive synchronization design for chaotic systems via a scalar during signal. IEEE Trans. on Circuits & Systems-I, 2002, 49(1): 17-26
[190] Martin A., Banavar J. R. Chaos, noise and synchronization. Physical Review Letters, 1994, 72: 1451-1454
[191] 刘锋，穆肇骊，邱祖廉．ROssler混沌系统的脉冲同步．物理学报，1999，48(7)：1198-1203
[192] 黄玮，张化光．一类混沌系统的脉冲控制同步，东北大学学报(自然科学版)，2004，25(11)：1027-1029
[193] Wang Y. W., Wen C. Y., Xiao J. W. Impulsive synchronization of Chua's oscillators via a single variable. Chaos, Solitons & Fractals, 2006, 29: 198-201
[194] Xie W., Wen C., Li Z. Impulsive control for the stabilization and synchronization of Lorenz systems, Physics Letters A, 2000, 275: 67-72
[195] 关新平，范正平，彭海朋．扰动情况下基于RBF网络的混沌系统同步．物理学报，2001，50(9)：1670-1674
[196] 吴忠强，谭拂晓，王绍仙．基于无源化的细胞神经网络超混沌系统同步．物理学报，2006，55(4)：1651-1658
[197] 王占山，张化光，王智良．一类混沌神经网络的全局同步，物理学报，2006，55(6)：2687-2693
[198] Ge S. S., Wang C. Synchronization of uncertain chaotic systems via backstepping design. The 3rd PACC, Shanghai, 2000, July 4-7: 594-598
[199] Deng B., Wang J., Fei X. Y. Synchronizing two coupled chaotic neurons in external electrical stimulation using backstepping control. Chaos, Solitons & Fractals 2006, 29: 182-189
[200] Tanaka K., Ikeda T., Kim E. Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI based designs. IEEE Trans. on Fuzzy Systems, 1998, 6(2): 250-265
[201] Lian K. Y., Chiu C. S., Chiang T. S. LMI-Based Fuzzy Chaotic Synchronization and communications. IEEE Trans. on Fuzzy Systems, 2001, 9(4): 539-553
[202] 祁荣宾，冯汝鹏，金一宁．基于输入-输出线性化方法实现混沌系统的同步．控制理论 与应用，2004，23(8)：12-15
[203] 陈从颜，宋文忠．混沌同步的变结构控制．控制与决策，2001，16(6)：937-939
[204] 刘福才，王娟，石淼，等．混沌系统的非线性连续预测变结构控制与同步．物理学报，2002，51(12)：2707-2712
[205] Liao T. L., Huang N. S. Control and synchronization of discrete-time chaotic systems via variable structure control technique. Physical Letters A, 1997, 234(4): 262-268
[206] Zhang H., Ma X. K., Liu W. Z. Synchronization of chaotic systems with parametric uncertainty using active sliding mode control. Chaos, Solitons & Fractals, 2004, 21(5): 1249-1257
[207] Li X. R., Zhao L. Y., Zhao G. Z. Sliding mode control for synchronization of chaotic systems with structure or parameters mismatching. 2005, 6A(6): 571-576
[208] Yan Z. Y. Generalized-type synchronization of hyperchaotic oscillators using a vector signal. Commum. Theor. Phys., 2005, 44(1): 72-78
[209] 孙克辉，张泰山．超混沌系统的多变量驱动误差反馈控制同步方法．中南大学学报(自然科学版)，2005，36(4)：653-657
[210] Yang T., Li X. F., Shao H. H. Chaotic synchronization using backstepping method with application to the chua's circuit and Lorenz systems. Proc. of Aanerican control conference, 2001: 25-27
[211] Herve D., Martin H. Chaos shift keying-modulation and demodulation of a chaotic carrier using self-synchronizing Chua's circuits. IEEE Trans. on Circuits & Systems-Ⅱ, 1993, 40 (10): 634-642
[212] Kolumban G., Chua L. O. The role of synchronization in digital communications using Chaos-Part Ⅲ: Performance bounds for correlation receivers. IEEE Trans. on Circuits & Systems-Ⅰ, 2000, 47 (12): 1673-1683
[213] Tam W. M., Francis C. M., Tse C. K. Analysis of bit error rates for multiple access CSK and DCSK communication systems. IEEE Trans. on Circuits & Systems-I, 2003, 50(5), 702-707
[214] Kocarev L. Communication with chaotic hide. Int. J. Bifurcation & Chaos, 1993, 3: 479
[215] Ricardo F., Ramon J. O., Gualberto S. P. A Chaos-Based Communication scheme via Robust Asymptotic Feedback. IEEE Trans. on Circuits & Systems-Ⅰ, 2001 10: 1161-1169
[216] Nan M. K., Wong C. N., Tsang K. F. Secure digital communication based on linearly synchronized chaotic maps. Physical Review A, 2000, 3: 61-68
[217] Yang T. Chua L. O. Secure communication via chaotic parameter modulation. IEEE Trans. on Circuits & Systems-I: 1996, 43(9): 817-819
[218] 李文化，王智顺，何振亚．用于跳频多址通信的混沌跳频码．通信学报．1996，17(6)：17-19
[219] 何迪，何晨，蒋铃鸽．二相与四相无限折叠混沌扩频序列的相关特性分析．通信学报，2001，22(3)：13-19
[220] 钟国群．蔡氏电路混沌同步保密通讯电路与系统学报．1996，1(1)：19
[221] 尹元昭．混沌同步和混沌保密通讯的实验研究．电子科学学刊．1998，20(1)：93-97
[222] 周小安，丘水生，陈艳峰．超混沌系统的一种同步方法，电路与系统学报，1999，4(4)：74-77
[223] 周红，罗杰，凌燮亭．关于数字混沌系统保密通信的探讨．电子科学学刊．1997，19(2)：202-208
[224] 蔡新国，丘水生．基于斜率调制的混沌通信系统，电子科学学刊，1999，21(3)：416-419
[225] Kocarev L., Parlitz. U. Generalized synchronization, predictability, and Equivalence of unidirectionally coupled dynamical systems. Physical Review Letters, 1996, 76(11): 1816-1819
[226] John R.T., Gregory D.V. Chaotic commtmication using generalized synchronization. Chaos, Solitons & Fractals, 2001, 12:145-152
[227] Lu J.G, Xi Y.G. Linear generalized synchronization of continuous-time chaotic systems. Chaos, Solitons & Fractals, 2003, 17:825-831
[228] Yu Y.G., Zhang S.C. Global synchronization of three coupled chaotic systems with ring connection. Chaos, Solitons & Fractals, 2005, 24(5): 1233-1242
[229] Guan Z.H., Liao R.Q., Zhou A. On impulsive control and its application to Chen's chaotic system. Int. J. Bifurcation & Chaos, 2002, 12(5): 1191-1197
[230] Qi J.G., Fu X.L. Existence of limit cycles of impulsive differential equations with impulses at variable times. Nonlinear Analysis, 2001, 44:345-353
[231] Smereka P.Synchronization of relaxation for a class of globally coupled Hamiltonian systems. Physica D, 1998, 124:104-125
[232] Chandrasekar J., Aaron R., Dennis S.B. A SDRE-based asymptotic observer for nonlinear discrete-time systems. 2005 American Control Conf., June 8-10, 2005:3630-3635
[233] Mracek C.P., Cloutier J.R. Control designs for the nonlinear Benchmark problem via the state-dependent Riccati equation method. Int. J. Robust and Nonlinear Control, 1998, 8(4): 401-433
[234] Erdem E.B. Analysis and real-time implementation of state-dependent Riccati equation controlled systems: [Doctor Degree Dissertation], USA, The University of Illinois, 2001
[235] Jayaram A., Tadi M. Synchronization of chaotic systems based on SDRE method. Chaos, Solitons & Fractals, 2006, 28:707-715
[236] 陈志盛，孙克辉，张泰山．Liu混沌系统的非线性反馈同步控制．物理学报，2005，54(6)：2580-2583
[237] 陈保颖．线性反馈实现Liu系统的混沌同步．动力学与控制学报，2006，4(1)：1-4
[238] 宁娣，陆君安．一个临界系统与Lorenz系统和Chen系统的异结构同步．物理学报，2005，54(10)：4590-4595
[239] Lu Z., Shieh L., Chen G.R. On robust control of uncertain chaotic systems a sliding mode synthesis via chaotic optimization. Chaos, Solitons & Fractals, 2003, 18:819-827
[240] Cheng C.C. Design of discrete quasi-sliding mode controllers with pertuabation estimation. IEEE Proc. of American Control Conference, 2000:621-625
[241] Azemi A., Yaz E.E. Sliding-mode adaptive observer approach to chaos synchronization. Journal of Dynamic Systems, Measurement and control, 2000, 122(4): 758-765
[242] Yang T., Shao H. Synchronizating chaotic dynamics with uncertainties based on a sliding mode control design. Physical Review E, 2002, 65:1-7
[243] Celikovsky S., Chen G.R. On the generalized Lorenz canonical form. Chaos, Solitons & Fractals, 2005, 26:1271-1276
[244] Celikovsky S., Chen G.R. Hyperbolic-type generalized Lorenz system and its canonical form. Proc. 15th Triennial World Congress of IFAC, Spain, 2002
[245] Kim E., Lee H. New approaches to relaxed quadratic stability condition of fuzzy control systems. Fuzzy Sets & Systems, 2000, 8(5): 523-534
[246] 佟绍成，柴天佑．一类多变量非线性动态系统的模糊鲁棒控制，自动化学报，2000，26(5)： 30-37
[247] Lee H.J., Park J.B., Chen G.R. Robust fuzzy control of nonlinear systems with parametric uncertainties. IEEE Trans, on Fuzzy Systems, 2001, 9(2): 369-379
[248] Tong S.C., Li H.X. Observer-based robust fuzzy control of nonlinear systems with parametric uncertainties. Fuzzy Sets & Systems, 2002, 131(2): 154-165
[249] Yoneyama J. H∞ control for Takagi-Sugeno fuzzy systems. Int. J. systems science, 2001, 32(7): 915-924
[250] Chen J., Liu Z.R. A Method of Controlling Synchronization in Diferent Systems, Chinese Physical Letters, 2003, 20(9): 1441
[251] Zhou T.S., Li C.P. Synchronization in fractional-order differential systems. Physica D: Nonlinear Phenomena, 2005,212(1): 111-125
[252] Bai E.W., Longgen K.E. Synchronization of two Lorenz systems using active control. Chaos, Solitons & Fractals, 2000,11: 1041-1044
[253] Li G.H. Generalized projective synchronization of two chaotic systems by using active control. Chaos, Solitons & Fractals, 2006, 30: 77-82
[254] Lei Y.M., Xu W., Shen J.W. Global synchronization of two parametrically excited systems using active control. Chaos, Solitons & Fractals, 2006, 28: 426-436
[255] Li G.H. An active control synchronization for two modified Chua circuits. Chinese Physics, 2005, 14(3): 472-475
[2] Hao B.L. Chaos Ⅱ. Singapore: World Scientific, 1990
[3] Lorenz E.N. Deterministic non-periodic flow. J. Atmos. Sci. 1963, 20:130-141
[4] Sivakumar B. Chaos theory in geophysics: past, present and future. Chaos, Solitons & Fractals, 2004, 19(2): 441-462
[5] Feigenbaum M,J. Quantitalive university for a class of nonlinear transformation. J. Star. Phys. 1978, 19:25-28
[6] Freeman W.H., Mandebort B.B. Fractal, form, chance and dimension. San Francisco, 1977
[7] Fleming W.H. Future directions in control theory: a mathematical perspective. SIAM Pub., 1988, 50-51
[8] Chen G.R., Dong X. From chaos to order: methodologies, perspectives and applications. Singapore: World Scientific, 1998
[9] Rossler O.E. An equation for continuous chaos. Physical Letters A, 1976, 57:397-398
[10] Chua L.O., Komuro M., Matsumoto T. The double scroll family. Part Ⅰ: rigorous proof of chaos. IEEE Trans. on Circuits & Systems-Ⅰ, 1986, 33: 1072-1096
[11] Chen G.R., Ueta T. Yet another chaotic attractor. Int. J. Bifurcation & Chaos, 1999, 9: 1465-1466
[12] Lu J.H., Chen G.R., Cheng D.Z. Bridge the gap between the Lorenz system and the Chen system. Int. J. Bifurcation & Chaos, 2002, 12(12): 2917-2926
[13] Lu J.H., Chen G.R., Yu X. Dynamical behaviors of a unified chaotic system, Dynamical of continuous, Discrete and Impulsive Systems Series B, 2003, Sup: 115-124
[14] Liu C.X,, Liu T., Liu L. A new chaotic attractor. Chaos, Solitons & Fractals, 2004, 22: 1031-1038
[15] Liu C.X., Liu L., Liu T. A new butterfly-shaped attractor of Lorenz-like system. Chaos, Solitons & Fractals, 2006, 28:1196-1203
[16] Wang F. Q., Liu C.X. Hyperchaos evolved from the Liu chaotic system. Chinese Physics, 2006, 15(5): 963-968
[17] Vanecek A., Celikovsky S. Control systems: From linear analysis to synthesis of chaos. London: Prentice Hall, 1996
[18] Lu J.H., Zhou T.S., Chen G.R., et al. Generating chaos with a switching piecewise-linear controller. Chaos, 2002, 12(2): 344-349
[19] Zheng Z.H., Lu J.H., Chen G.R., et al. Generating two simultaneously chaotic attractors with a switching piecewise-linear controller. Chaos, Solitons & Fractals, 2004, 20:277-288
[20] Li T.Y., Yorke J.A. Period three implies chaos. Amer. Math. Monthly, 1975, 82:985-992
[21] 关新平，范正平，陈彩莲．混沌控制及其在保密通信中的应用．北京：国防工业出版社，1993
[22] 方锦清，赵耿，罗晓曙．混沌保密通信应用研究的进展．广西师范大学学报(自然科学版)，2002，20(1)：6-18
[23] Windell H.O. Atom optics experiments in quantum chaos: [Doctor Degree Dissertation], USA, The University of Texas, 2001
[24] Gong J.B. Coherent control, quantum chaos, and decoherence in molecula: [Doctor Degree Dissertationl, Canada, University of Toronto, 2001
[25] 王光瑞，于煦龄，陈式刚．混沌的控制、同步和利用．北京：国防工业出版社，2001
[26] 邹恩，李详飞，陈建国等著．混沌控制及其优化应用．长沙：国防科技大学出版社，2002
[27] Iasonas K., Petros M. Nonlinear speech analysis using models for chaotic systems. IEEE Trans. on Speech & Audio Processing, 2005, 13(6): 1098-1109
[28] Feng J.C., Tse C.K., Francis C.M. A neural-network-based channel-equalization strategy for chaos-based communication systems. IEEE Trans. on Circuits & System-I, 2003, 50(7): 954-957
[29] Alexander L.B., Wolfgang S. Chaotic and random point processes: analysis, design, and applications to switching systems. IEEE Trans. on Circuits & System-I, 2003, 50(8): 1081-1088
[30] 覃团发，唐秋玲，姚海涛．实时数字语音混沌保密通信系统．计算技术与自动化，2000，19(1)：58-61
[31] 李昌刚，韩正之．一种基于离散混沌系统的密钥流设计算法，信息与控制，2002，31(5)：407-411
[32] Chen L., Aihara K. Global search ability of chaotic neural networks. IEEE Trans. on Circuits & Systems-I, 1999, 46(8): 974-993
[33] Ma W., Wang Z.O. A new chaotic parameters annealing neural network for solving global optimization problems. Comlnun. Theor. Phys., 2003, 39(4): 385-392
[34] 骆晨钟，邵惠鹤．用混沌搜索求解非线性约束优化问题．系统工程理论与实践，2002，8：54-57
[35] 李兵，蒋慰孙．混沌优化方法及其应用．控制理论与应用，1997，14(4)：613-615
[36] 孟红记，郑鹏，梅国晖．基于混沌序列的粒子群优化算法．控制与决策，2005，21(3)：263-266
[37] 张彤，王宏伟，王子才．变尺度混沌优化方法及其应用．控制与决策，1999，14(3)：285-288
[38] Sabri A. Global asymptotic stability of a class of dynamical neural networks. IEEE Trans. on Circuits & Systems-I, 2000, 47(4): 568-571
[39] Qiu S.S. A cell model of chaotic attractor. Proceedings IEEE ISCAS'97, HongKong, 1997
[40] 王凌，郑大钟．一种基于退火策略的混沌神经网络优化算法．控制理论与应用，2000，17(1)：139-142
[41] 陈冬，戴琼海，徐文立，引入混沌机制处理HFC网络回传噪声问题．清华大学学报(自然科学版)，2002，42(11)：1556-1559
[42] 蒋传文，权先璋，李承军，张勇传．混沌理论在电力负荷预测中的应用，武汉交通科技大学学报，1999，23(61：609-612
[43] 薛禹胜，周海强，顾晓荣．电力系统分岔与混沌研究述评，电子系统自动化，2002，26(16)：9-15
[44] 张波，李忠，毛宗源．永磁同步电动机的混沌特性及其反混沌控制．控制理论与应用，2002，19(4)：545-548
[45] Ott E., Grebogi C., Yorke J.A. Controlling chaos, Physical Review Letters, 1990, 64(11): 1196-1199
[46] Gallego J.A. Nonlinear regulation of a Lorenz system by feedback linearization techniques. Dynamic Control, 1994, 4:277-298
[47] Chen G.R., Dong X. On feedback control of chaotic continuous-time systems. IEEE Trans. on Circuits & Systems, 1993, 40(9): 591-601
[48] Chen G.R., Dong X. Controlling Chua's system. J. Circuits, Systems & Computations, 1993, 3:139-148
[49] Naumenko A.V., loiko N.A., Turovets S.I. Chaos control in external cavity laser diodes using electroni impulsive delayed feedback. Int. J. Bifuracation & Chaos, 1996, 6:1791-1799
[50] 李伟，陈式刚．用周期拍方法控制非线性耗散系统和保守系统的混沌，物理学报，2001，50(10)：1862-1870
[51] Yu Y.G., Zhang S.C. Adaptive backstepping control of the uncertain Lu system. Chinese Physics, 2002, 12(11): 1249-1253
[52] 张思进，陆启韶，王士敏．碰摩转子映射系统的延迟反馈混沌控制．固体力学学报，2001，22(3)：89-94
[53] Chen L. Predictive fuzzy control of uncertain chaotic systems: [Doctor degree dissertation], USA, University of Houston, 1998
[54] Li Z, Han C.Z. Adaptive control and identification of chaotic systems. Chinese Physics, 2001, 10(6):494-496
[55] 李智，韩祟昭．一类含参数不确定性混沌系统的自适应控制，物理学报，2001，50(5)：847-850
[56] 王中生，何汉林，廖晓昕．含多参数的不确定线性时滞系统的鲁棒镇定．华中科技大学学报，2003，31(5)：36-38
[57] 张毅锋，何振亚，杨绿溪．用脉冲控制法抑制非自治细胞神经网络中的混沌．控制与决策，1999，14(5)：418-422
[58] 罗晓曙．非线性系统中的混沌控制与同步及其应用研究：[博士学位论文]，北京：中国科学技术大学，2003
[59] Luo X.S., Wang B.H., Jiang F. Using random proportional pulse feedback of system variables to control chaos and hyperchaos. Chinese Physics, 2001, 10(1): 17-20
[60] Luo X.S., Fang J.Q. A method of controlling spatiotemporal chaos in coupled map lattices. Chinese Physics, 2000, 9(5): 333-336
[61] 薛月菊，冯汝鹏．连续时间耦合系统中时空混沌的自适应模糊控制．物理学报，2001，50(3)：440-444
[62] 方天华．超混沌同步的非线性控制法．原子能科学技术，1998，32(2)：184-187
[63] Vincent T.L., Yu J. Control of a chaotic System. Dynamic Control, 1991, 1:35-52
[64] Zhang Y., Wen C., Sob Y.C. Discrete-time robust backstepping adaptive control for nonlinear time-varying systems. IEEE Trans. on Automatic Control, 2000, 45:1749-1755
[65] Lu J.H, Lu J.A. Controlling uncertain Lu system using linear feedback. Chaos, Soliton & Fractals, 2003, 17(1): 127-133
[66] Lu J.H, Zhou T., Zhang S. Controlling Chen system using feedback function based on parameters identification. Chinese Physics, 2002, 12(10): 2257-2270
[67] 吴忠强，赵海英．一种模糊滑模变结构控制方案及其在混沌系统控制中的应用．信息与控制，2002，31(3)：280-283
[68] Gohary A.E., Yassen R. Adaptive control and synchronization of a conpled dynamo system with uncertain parameters. Chaos, Solitons & Fractals, 2006, 29:1085-1094
[69] Zou Y.L., Zhu J. Controlling the chaotic n-scroll Chua's c(?)cuit with two low-pass filters. Chaos, Solitons & Fractals, 2006, 29:400-406
[70] Barbara C., Silvano C., Alessandro P.Controlling chaos via second-order sliding modes. ISCAS 2003．Ⅲ：156-159
[71] 张晓辉，沈柯．高周期混沌轨道的构造方法和应用，物理学报，1999，48(12)：2186-2190
[72] Yang L., Liu Z. R. and Mao J. Controlling hyperchaos, Physical Review Letters, 2004, 84: 67
[73] Guan X. P., Hua C. C., Duan G. R. Comments on "Robust stabilization of a class of time-delay nonlinear systems". IEEE Trans. on Automatic Control, 2003, 48(5): 907-908
[74] Liu G. G., Zhao Y. Adaptive control on a class of uncertain chaotic systems. Chinese Physical Letters, 2005, 22(5): 1069-1071
[75] Tsui A. P., Jones A. J. The control of higher dimensional chaos: comparative results for the chaotic satellite attitude control problem. Physica D, 2000, 135: 41-62
[76] Lu J. A., Xie J., Lu J. H. Control chaos in transition system using sampled-data feedback. Applied Methematics & Mechanics, 2003, 24(11): 1309-1316
[77] Yu H. J., Lin Y. Z., Peng J. H. Continuous control of chaos based on the stability criterion. Physical Review E, 2004, 69(62): 066203
[78] Wang Z. S., Liao X. X. Adaptive synchronization and parameter identification for a unified chaotic system. 2004 Int. Conf. Information Acquisition, 2004: 20-22
[79] Yu D. C., Wu A. G., Wang D. Q. A simple asymptotic trajectory control of full sates of a unified chaotic system. Chinese Physics, 2006, 15(2): 306-309
[80] 修春波，刘向东，张宇河．混沌优化与模糊控制在混沌控制中的应用．控制理论与应用，2005，22(1)：63-67
[81] Pecora L. M., Carroll T. L. Synchronization in chaotic systems. Physical Review Letters, 1990, 64(8): 821-825
[82] Chert G. R., Lai D. Feedback control of Lyapunov exponents for dynamic systems. Int. J. Bifurcation & Chaos, 1996, 6: 1341-1349
[83] Wang X. F., Chen G. R. Chaotifying a stable LTI system by tiny feedback control. IEEE Trans. on Circuits & Systems, 2000, 47: 410-415
[84] Wang X. F., Chen G. R. Chaotifying a stable map via smooth small-amplitude high-frequency feedback control. Int. J. Circuit Theory & Application, 2000, 28: 305-312
[85] Wang X. F., Chen G. R., Yu X. Anticontrol of chaos in continuous-time systems via time-delay feedback. Chaos, 2000, 1: 771-779
[86] 卢俊国．混沌同步与反控制的若干问题研究：[博士后工作报告]，上海：上海交通大学，2003
[87] 甘春标，郭乙木．拟可积哈密顿系统中噪声诱发的混沌运动，力学学报，2000，32(5)：613-620
[88] Tang K. S., Man K.E, Zhong G. Q. Generating chaos via x|x|. IEEE Trans. on Circuits & Systems-Ⅰ: 2001, 48(5): 636-641
[89] Li Y. X., Chen G. R., Wallace K. S. Controlling a unified chaotic system to hyperchaotic. IEEE Trans. on Circuit & Systems-H, 2005, 52(4): 204-207
[90] Codreanu S. Desynchronization and chaotification of nonlinear dynamical systems. Chaos, Solitons & Fractals, 2002, 13: 839-843
[91] Potapov A., Ali M. K. Chaotic Neural Control. Physical Review E63: 046215
[92] Sanchez E. N., Perez J. P., Chert G. R. Using dynamic neural network to generate chaos: an inverse optimal control approach. Int. J. Bifurcation & Chaos, 2001, 11: 857-863
[93] Chen G. R., Yang L., Liu Z. R. Anticontrol of chaos for continuous-time systems. IEICE Trans. on Fundamentals of Electronics, Communications and Computer Sciences, 2002, E85A(6): 1333-1335
[94] 张丽丽，张晓丹．四维线性微分系统的混沌反控制理论及应用．北京科技大学学报，2004，26(6)：673-677
[95] 朱淑芹，杨淼，张先华，闵乐泉．利用Silnikov定理构造混沌系统．北京科技大学学报，2005，27(5)：636-638
[96] Salama K.N., Ozoguz S., Elwakil A.S. Generation of n-scroll chaos using nonlinear transconductors. ISCAS 2003, Ⅲ: 176-179
[97] Wallace K.S., Tang G.Q., Chen Z.G. Generation of n-scroll attractors via sine function. IEEE Trans. on Circuits & Systems-I: 2001, 48(11): 1369-1372
[98] Wang J.Z., Chen Z.Q., Yuan Z.Z. The generation of a hyperchaotic system based on a three-dimensional autonomous chaotic system. Chinese Physics, 2006, 15(6): 1216-1225
[99] Li X., Chert Z.Q., Yuan Z.Z. Generating Chaos by an Elman Network. IEEE Trans. on Circuits & systems-I, 2001, 48(11): 1126-1131
[100] Lin W., Ruan J., Zhao W.R. On the mathematical clarification of the snap-back-repeller in high-dimensional system and chaos in a discrete neural network model. Int. J. Bifurcation & Chaos, 2002, 12(5): 1129-1139
[101] 王兴元，杨威，边丽英．构造广义Rossler奇怪吸引子的一种新方法，东北大学学报(自然科学版)，2001，22(3)：261-264
[102] Liu Z.R., Chung K.W. Hybrid control of bifurcation in continuous nonlinear dynamical systems. Int. J. of Bifurcation and Chaos, 2005, 15(I2): 3895-3903
[103] Radoslav R., Elena V., Chen G.R. Local bang-bang control of a chaotic system with two 2-scroll attractors. Dynamic of Continuous Discrete and Impulsive Systems Series B, 2004, 11a: 152-158
[104] Lu J.A., Tao C.H. Parameter identification and tracking of a unified system. Chinese Physical Letters, 2002, 19 (5): 632-635
[105] 关新平，范正平，龙承念．非线性不确定时滞混沌系统的鲁棒控制．控制理论与应用，2002，19(2)：211-214
[106] Kuang Y.L., Liu P., Wei C.L. Robust chaotic fuzzy output tracking control. IEEE Int. Fuzzy Systems Conference, 2001: 1577-1580
[107] Lewis C.T. Issues in chaos synchronization: subhannonic destruction, multi-valued mappings, and chaotic lightwave communication: [Doctor degree dissertation], USA, University of California, 2001
[108] Li X.J., Zhang Y., Du G.H. An investigation on chaotic behavior of two forms of ray eouations, J. of Nanjing University (Natural Sciences), 2000, 36(3): 383-386
[109] 文成秀，赵长宽，闻邦椿．分段线性振动机械关于外激振频率的分岔与混沌，东北大学学报(自然科学版)，2001，22(2)：200-202
[110] 戴栋，马西奎，李小峰．一类具有两个边界的分段光滑系统中边界碰撞分岔现象及混沌，物理学报，2003，52(11)：2729-2736
[111] Brown R., Kocarev L. A unifying definition of synchronization for dynamical systems. Chaos, 2000, 10(2): 344-349
[112] Yan Z.Y. Q-S(lag or anticipated) synchronization backstepping scheme in a class of continuous-time hyperchaotic system. Chaos, 2005, 15:023902
[113] Yah Z.Y. Chaos Q-S synchronization between Rossler system and the new unified chaotic system. Physical Letters A, 2005, 334:406
[114] 陶朝海，陆君安，吕金虎．统一混沌系统的反馈同步．物理学报，2002，51(7)：1497-1501
[115] Lu J.G. Chaotic dynamics and synchronization of fractional-order Arneodo's systems. Chaos, Solitons & Fractals, 2005, 26(4): 1125-1133
[116] 王福田，洪奕光．关于混沌系统的鲁棒和自适应同步化．控制理论与应用，2000，17(3)：55-59
[117] Alexander E.H., Alexey A.K. An approach to chaotic synchronization. Chaos, 14(3): 603-610
[118] Li Y.N., Chen L. Cai Z.S. Chaos synchronization in the Belousov-Zhabotinsky reaction by adaptive control scheme. Chinese Journal of Chemistry, 2002, 20:753-759
[119] Liu W.B., Chen G.R. Control and synchronization of a 4-scroll chaotic system. ISCAS 2003, Ⅲ: 100-103
[120] Li F., Hu A.H. Xu Z.Y. Robust synchronization of uncertain chaotic systems. Chinese Physics, 2006, 15(3): 507-512
[121] Williams C. A robust chaotic communications system based on generalized synchronization. 1998 IEEE Int. Conf. on Electronics, Circuits and Systems, 1998:243-246
[122] Wang Y.W., Guan Z.H. Generalized synchronization of continuous chaotic system. Chaos, Solitons & Fractals, 2006, 27(1): 97-101
[123] Shahverdiev E.M., Sivaprakasam S., Shore K.A. Lag synchronization in time delayed system. Physical Review A, 2002, 292(6): 320-324
[124] Taherion S., Lai Y.C. Observability of lag synchronization of coupled chaotic oscillators. Physical Review E, 1999, 59(6): 6247-6250
[125] Chen J.Y., Wong K.W. Phase synchronizationin discrete chaotic systems. Physical Review E, 2000, 61(3): 2559-2562
[126] 桑海波，贺凯芬．用外加周期信号控制时空混沌中的相同步．北京师范大学学报(自然科学版)，2004，40(3)：350-353
[127] Yan Z.Y. Q-S synchronization in 3D Henon-like map and generalized Henon map via a scalar controller. Physics Letters A, 2005, 342:309-317
[128] 程丽，张入元，彭建华．用单一驱动变量同步混沌与超混沌的一种方法．物理学报，2003，52(3)：536-541
[129] Kocarev L., Parlitz U. General approach for chaotic synchronization with applications to communication. Physical Review Letters, 1995, 74: 5028-5031
[130] Surkens J.A., Curren P E., Chua L.O. Robust synthesis for master-slave synchronization of Lur'e systems. IEEE Trans. on Circuits & Systems-I, 1999, 46(7):841-850
[131] 罗晓曙，方锦清．用离散混沌信号驱动实现混沌同步．物理学报，1999，48(11)：2022-2028
[132] Wang R., Shen K. Synchronization of chaotic erbium-doped fiber dual-ring lasers by using the method of another chaotic system to drive them. Physical Review E, 2002, 65(1): 016207
[133] 赖建文，周世平，李国辉，等．间歇驱动混沌同步法．物理学报，2001，50(1)：21-25
[134] 肖宏芳，黄祖达．半线性驱动-响应系统在输出反馈控制下的混沌同步．数学理论与应用，2005，25(4)：72-74
[135] Stojanovski T., Kocarev L., Parlitz U. Spiradic driving of dynamical systems. Physical Review E, 1997, 55(4): 4035-4047
[136] Kocarev L., Parlitz U., Stojanovski T. Chaos synchronization using sporadic driving. Physical D, 1997, 109:139-152
[137] 杨世平，牛海燕，田钢，等．用驱动参量法实现混沌系统的同步．物理学报，2001，50(4)：619-623
[138] Pyragas K. Continous control of chaos by self-controlling systems. Physical Letters A, 1992, 170:421-428
[139] Pyragas K., Tamasevicius A. Experimental control of chaos by delayed selfcontrolling feedback. Physical Letters A, 1993,180: 99-102
[140] 唐芳，邱琦．混沌系统的辅助参考反馈控制．物理学报，1999，48(5)：802-807
[141] Jiang G.P., Tang K.S. A global synchronization criterion for coupled chaotic systems via unidirectional linear error feedback approach. Int. J. Bifurcation Chaos, 2002, 12(10): 2239-2253
[142] Bu S.L., Wang S.Q., Ye H.Q. An algorithm based on variable feedback to synchronize chaotic and hyperchaotic systems. Physica D, 2002, 164:45-52
[143] 高金峰，罗先觉，马西奎．控制与同步连续时间混沌系统的非线性反馈方法，物理学报，1999，48(9)：1618-1627
[144] 刘扬正，费树岷．Genesio-Tesi和Coullet混沌系统之间的非线性反馈同步．物理学报，2005，54(8)：3486-3490
[145] 陶朝海，陆君安．混沌系统的速度反馈同步．物理学报，2005，54(11)：5058-5061
[146] Hang F. L. Yu X.H., Feng Y. A further study of nonlinear feedback system with chaotic oscillation. WCICA 2004-Fifth World Congress on Intelligent Control and Automation, 2004: 83-86.
[147] Roy R. Experimental synchronization of chaos. Physical Review Letters, 1994, 72(13): 2009-2012
[148] Sugawara T. Observation of synchronization in laser chaos. Physical Review Letters, 1994, 72(22): 3502-3505
[149] Kapitaniak T. Experimental synchronization of chaos using continuous control. Int. J. Bifirurcation & Chaos, 1994, 4(2): 483-488
[150] Angeli A.D., Chua L.O. Dead-Beat chaos synchronization in discrete-time systems. IEEE Trans. on Circuits & Systems, 1995, 2(1): 54-56
[151] Wn C,W., Chua L.O. Synchronization in and array of linearly coupled dynamical systems. IEEE Trans. on Circuits & Systems-I, 1995, 42(8): 430-447
[152] 蒋品群，汪秉宏，罗晓曙．四阶蔡氏超混沌电路的单向耦合同步研究．系统工程与电子技术，2004，25(9)：119-1121
[153] 张旭，沈柯．时空混沌的单向耦合同步，物理学报，2002，51(12)：2702-2706
[154] Lu J.H., Zhou T.S., Zhang S.C. Chaos synchronization between linearly coupled chaotic systems. Chaos, Solitons & Fractals, 2002, 14:529-541
[155] Li D.M., Lu J.A., Wu X.Q. Linearly coupled synchronization of the unified chaotic systems and the Lorenz systems. Chaos, solitons & Fractals, 2005, 23:79-85
[156] Ju H.P. Stability criterion for synchronization of linearly coupled unified chaotic systems, Chaos, Solitons & Fractals, 2005, 23:1319-1325
[157] 闵富红，王执铨．统一混沌系统的耦合同步．物理学报，2005，54(9)：4026-4030
[158] 卢俊国，汪小帆，王执铨．连续时间混沌系统控制与同步的状态反馈方法．控制与决策， 2001，16(4)：476—479
[159] 张宇，余俊明，杜功焕．连续反馈混沌同步方式在保密通讯的中应用．科学通报，1998，43(17)：1831-1835
[160] Bai E.W., Lonngren K.E. Sequential synchronization of two Lorenz systems using active control. Chaos, Solitons & Fractals, 2000, 11: 1041-1044
[161] Kouomou Y.C., Woafo P. Stability and optimization of chaos synchronization through feedback coupling with delay. Physics Letters A, 2002, 298:18-28
[162] 戴旭初，张锦钢，徐佩霞．一种基于耦合反馈的离散组合混沌系统的同步方法．控制理论与应用，2000，17(5)：789-792
[163] Morgul O., Solak E. On the synchronization of chaotic systems by using state observations. Int. J. Bifurcation & Chaos, 1997, 7(6): 1307-1322
[164] Nijmeijer H., Mareeis I.M. An Observer Looks at Synchronization. IEEE Trans. on Circuits & Systems-I, 1997, 44(10): 882-890
[165] 李世华，蔡海兴．Chen氏混沌电路实现与同步控制实验研究．物理学报，2004，53(6)：1687-1693
[166] 张学义，李殿璞，陈实如．基于状态观测器超混沌系统高精度保密通信方法．电路与系统学报，2001，6(4)：5-18
[167] 杨涛，邵惠鹤．一类混沌系统的同步方法．物理学报，2002，51(4)：742-748
[168] Boutayeb M., Darouach M., Rafaralyahy H. Generalized state-space observers for chaotic synchronization and secure commtmication. IEEE. Trans. Circuits & Systems-I, 2002, 49(3): 345-349
[169] Wang W.W., Gao Z.Q. A comparison study of advanced state observer design teclmiques. Proceedings of the American Control Conference, Colorado, 2003, June 4-6
[170] 姚利娜，高金峰，廖旎焕．实现混沌系统同步的非线性状态观测器方法．物理学报，2006，55(1)：35-41
[171] Li G.H., Zhou S.P., Xu D.M. Chaos synchronization based on intermittent state observer. Chinese Physics, 2004, 13(2): 168-172
[172] Jolly K.J., Amritkar R.E. Synchronization of unstable orbits using adaptive control. Physical Review E, 1994, 94:4883
[173] Fradkov A.L., Pogromsky Y.A. Speed gradient control of chaotic continuous-time systems. IEEE Trans. on Circuits & Systems-I: 1996, 43(11): 907-913
[174] Andrievsky B. Adaptive synchronization methods for signal transmission on chaotic carriers. Mathematics and Computers in Simulation, 2002, 58:289-293
[175] Liao T.L., Tsai S.H. Adaptive synchronization of chaotic systems and its application to secure communications. Chaos, Solitons & Fractals, 2000, 11:1387-1396
[176] Femat R., Alvarez R.J., Fernendez A.G. Adaptive synchronization of high-order chaotic systems: a feedback with low-order parametrization. Physica D, 2000, 139:231-246
[177] 齐冬莲，魏金岭，赵光宙．基于系统辨识的自适应混沌同步控制研究，控制与决策，2001，16(5)：120-122
[178] Wang C., Ge S.S. Adaptive synchronization of uncertain chaotic systems via backstepping design. Chaos Solitons & Fractals, 2001, 12:1119-1206
[179] Dai D., Ma X.K. Chaos synchronization by using intermittent parametric adaptive control method. Physics Letters A, 2001, 288:23-28
[180] 关新平，陈彩莲，范正平．基于backstepping方法的混沌系统自适应模糊控制．物理学报，2002，51(4)：753-758
[181] 范正平．混沌控制、同步及在保密通信中的应用：[博士学位论文]，河北：燕山大学，2003
[182] Wang Z. L., Zhang H. G. Adaptive synchronization of discrete chaotic systems, Proceedings of 2002 Int. Conf. on Machine Learning and Cybernetics, 2002: 336-339
[183] 樊春霞，姜长生．统一混沌系统自适应同步控制．系统工程与电子技术，2004，26(3)：358-360
[184] 孙克辉，陈志盛，张泰山．基于参数自适应方法的统一混沌系统的同步控制．信息与控制，2005，34(1)：40-43
[185] Wang Y. W., Guan Z. H. Adaptive synchronization for Chen chaotic system with fully unknown parameters. Chaos, Solitons & Fractals, 2004, 19(4): 899-903
[186] Wang Z. S., Liao X. X. Synchronization and parameters identification of chaotic systems via adaptive control. J. of Electronic Science and Technology of China, 2005, 3(1): 64-67
[187] 刘国刚，赵怡．参数不确定混沌系统的自适应同步控制，电路与系统学报，2005，10(1)：24-27
[188] 王兴元，武相军．不确定Chen系统的参数辨识与自适应同步，物理学报，2006，55(2)：605-609
[189] Kuang Y. L., Peter L., Tung S. C. Adaptive synchronization design for chaotic systems via a scalar during signal. IEEE Trans. on Circuits & Systems-I, 2002, 49(1): 17-26
[190] Martin A., Banavar J. R. Chaos, noise and synchronization. Physical Review Letters, 1994, 72: 1451-1454
[191] 刘锋，穆肇骊，邱祖廉．ROssler混沌系统的脉冲同步．物理学报，1999，48(7)：1198-1203
[192] 黄玮，张化光．一类混沌系统的脉冲控制同步，东北大学学报(自然科学版)，2004，25(11)：1027-1029
[193] Wang Y. W., Wen C. Y., Xiao J. W. Impulsive synchronization of Chua's oscillators via a single variable. Chaos, Solitons & Fractals, 2006, 29: 198-201
[194] Xie W., Wen C., Li Z. Impulsive control for the stabilization and synchronization of Lorenz systems, Physics Letters A, 2000, 275: 67-72
[195] 关新平，范正平，彭海朋．扰动情况下基于RBF网络的混沌系统同步．物理学报，2001，50(9)：1670-1674
[196] 吴忠强，谭拂晓，王绍仙．基于无源化的细胞神经网络超混沌系统同步．物理学报，2006，55(4)：1651-1658
[197] 王占山，张化光，王智良．一类混沌神经网络的全局同步，物理学报，2006，55(6)：2687-2693
[198] Ge S. S., Wang C. Synchronization of uncertain chaotic systems via backstepping design. The 3rd PACC, Shanghai, 2000, July 4-7: 594-598
[199] Deng B., Wang J., Fei X. Y. Synchronizing two coupled chaotic neurons in external electrical stimulation using backstepping control. Chaos, Solitons & Fractals 2006, 29: 182-189
[200] Tanaka K., Ikeda T., Kim E. Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI based designs. IEEE Trans. on Fuzzy Systems, 1998, 6(2): 250-265
[201] Lian K. Y., Chiu C. S., Chiang T. S. LMI-Based Fuzzy Chaotic Synchronization and communications. IEEE Trans. on Fuzzy Systems, 2001, 9(4): 539-553
[202] 祁荣宾，冯汝鹏，金一宁．基于输入-输出线性化方法实现混沌系统的同步．控制理论 与应用，2004，23(8)：12-15
[203] 陈从颜，宋文忠．混沌同步的变结构控制．控制与决策，2001，16(6)：937-939
[204] 刘福才，王娟，石淼，等．混沌系统的非线性连续预测变结构控制与同步．物理学报，2002，51(12)：2707-2712
[205] Liao T. L., Huang N. S. Control and synchronization of discrete-time chaotic systems via variable structure control technique. Physical Letters A, 1997, 234(4): 262-268
[206] Zhang H., Ma X. K., Liu W. Z. Synchronization of chaotic systems with parametric uncertainty using active sliding mode control. Chaos, Solitons & Fractals, 2004, 21(5): 1249-1257
[207] Li X. R., Zhao L. Y., Zhao G. Z. Sliding mode control for synchronization of chaotic systems with structure or parameters mismatching. 2005, 6A(6): 571-576
[208] Yan Z. Y. Generalized-type synchronization of hyperchaotic oscillators using a vector signal. Commum. Theor. Phys., 2005, 44(1): 72-78
[209] 孙克辉，张泰山．超混沌系统的多变量驱动误差反馈控制同步方法．中南大学学报(自然科学版)，2005，36(4)：653-657
[210] Yang T., Li X. F., Shao H. H. Chaotic synchronization using backstepping method with application to the chua's circuit and Lorenz systems. Proc. of Aanerican control conference, 2001: 25-27
[211] Herve D., Martin H. Chaos shift keying-modulation and demodulation of a chaotic carrier using self-synchronizing Chua's circuits. IEEE Trans. on Circuits & Systems-Ⅱ, 1993, 40 (10): 634-642
[212] Kolumban G., Chua L. O. The role of synchronization in digital communications using Chaos-Part Ⅲ: Performance bounds for correlation receivers. IEEE Trans. on Circuits & Systems-Ⅰ, 2000, 47 (12): 1673-1683
[213] Tam W. M., Francis C. M., Tse C. K. Analysis of bit error rates for multiple access CSK and DCSK communication systems. IEEE Trans. on Circuits & Systems-I, 2003, 50(5), 702-707
[214] Kocarev L. Communication with chaotic hide. Int. J. Bifurcation & Chaos, 1993, 3: 479
[215] Ricardo F., Ramon J. O., Gualberto S. P. A Chaos-Based Communication scheme via Robust Asymptotic Feedback. IEEE Trans. on Circuits & Systems-Ⅰ, 2001 10: 1161-1169
[216] Nan M. K., Wong C. N., Tsang K. F. Secure digital communication based on linearly synchronized chaotic maps. Physical Review A, 2000, 3: 61-68
[217] Yang T. Chua L. O. Secure communication via chaotic parameter modulation. IEEE Trans. on Circuits & Systems-I: 1996, 43(9): 817-819
[218] 李文化，王智顺，何振亚．用于跳频多址通信的混沌跳频码．通信学报．1996，17(6)：17-19
[219] 何迪，何晨，蒋铃鸽．二相与四相无限折叠混沌扩频序列的相关特性分析．通信学报，2001，22(3)：13-19
[220] 钟国群．蔡氏电路混沌同步保密通讯电路与系统学报．1996，1(1)：19
[221] 尹元昭．混沌同步和混沌保密通讯的实验研究．电子科学学刊．1998，20(1)：93-97
[222] 周小安，丘水生，陈艳峰．超混沌系统的一种同步方法，电路与系统学报，1999，4(4)：74-77
[223] 周红，罗杰，凌燮亭．关于数字混沌系统保密通信的探讨．电子科学学刊．1997，19(2)：202-208
[224] 蔡新国，丘水生．基于斜率调制的混沌通信系统，电子科学学刊，1999，21(3)：416-419
[225] Kocarev L., Parlitz. U. Generalized synchronization, predictability, and Equivalence of unidirectionally coupled dynamical systems. Physical Review Letters, 1996, 76(11): 1816-1819
[226] John R.T., Gregory D.V. Chaotic commtmication using generalized synchronization. Chaos, Solitons & Fractals, 2001, 12:145-152
[227] Lu J.G, Xi Y.G. Linear generalized synchronization of continuous-time chaotic systems. Chaos, Solitons & Fractals, 2003, 17:825-831
[228] Yu Y.G., Zhang S.C. Global synchronization of three coupled chaotic systems with ring connection. Chaos, Solitons & Fractals, 2005, 24(5): 1233-1242
[229] Guan Z.H., Liao R.Q., Zhou A. On impulsive control and its application to Chen's chaotic system. Int. J. Bifurcation & Chaos, 2002, 12(5): 1191-1197
[230] Qi J.G., Fu X.L. Existence of limit cycles of impulsive differential equations with impulses at variable times. Nonlinear Analysis, 2001, 44:345-353
[231] Smereka P.Synchronization of relaxation for a class of globally coupled Hamiltonian systems. Physica D, 1998, 124:104-125
[232] Chandrasekar J., Aaron R., Dennis S.B. A SDRE-based asymptotic observer for nonlinear discrete-time systems. 2005 American Control Conf., June 8-10, 2005:3630-3635
[233] Mracek C.P., Cloutier J.R. Control designs for the nonlinear Benchmark problem via the state-dependent Riccati equation method. Int. J. Robust and Nonlinear Control, 1998, 8(4): 401-433
[234] Erdem E.B. Analysis and real-time implementation of state-dependent Riccati equation controlled systems: [Doctor Degree Dissertation], USA, The University of Illinois, 2001
[235] Jayaram A., Tadi M. Synchronization of chaotic systems based on SDRE method. Chaos, Solitons & Fractals, 2006, 28:707-715
[236] 陈志盛，孙克辉，张泰山．Liu混沌系统的非线性反馈同步控制．物理学报，2005，54(6)：2580-2583
[237] 陈保颖．线性反馈实现Liu系统的混沌同步．动力学与控制学报，2006，4(1)：1-4
[238] 宁娣，陆君安．一个临界系统与Lorenz系统和Chen系统的异结构同步．物理学报，2005，54(10)：4590-4595
[239] Lu Z., Shieh L., Chen G.R. On robust control of uncertain chaotic systems a sliding mode synthesis via chaotic optimization. Chaos, Solitons & Fractals, 2003, 18:819-827
[240] Cheng C.C. Design of discrete quasi-sliding mode controllers with pertuabation estimation. IEEE Proc. of American Control Conference, 2000:621-625
[241] Azemi A., Yaz E.E. Sliding-mode adaptive observer approach to chaos synchronization. Journal of Dynamic Systems, Measurement and control, 2000, 122(4): 758-765
[242] Yang T., Shao H. Synchronizating chaotic dynamics with uncertainties based on a sliding mode control design. Physical Review E, 2002, 65:1-7
[243] Celikovsky S., Chen G.R. On the generalized Lorenz canonical form. Chaos, Solitons & Fractals, 2005, 26:1271-1276
[244] Celikovsky S., Chen G.R. Hyperbolic-type generalized Lorenz system and its canonical form. Proc. 15th Triennial World Congress of IFAC, Spain, 2002
[245] Kim E., Lee H. New approaches to relaxed quadratic stability condition of fuzzy control systems. Fuzzy Sets & Systems, 2000, 8(5): 523-534
[246] 佟绍成，柴天佑．一类多变量非线性动态系统的模糊鲁棒控制，自动化学报，2000，26(5)： 30-37
[247] Lee H.J., Park J.B., Chen G.R. Robust fuzzy control of nonlinear systems with parametric uncertainties. IEEE Trans, on Fuzzy Systems, 2001, 9(2): 369-379
[248] Tong S.C., Li H.X. Observer-based robust fuzzy control of nonlinear systems with parametric uncertainties. Fuzzy Sets & Systems, 2002, 131(2): 154-165
[249] Yoneyama J. H∞ control for Takagi-Sugeno fuzzy systems. Int. J. systems science, 2001, 32(7): 915-924
[250] Chen J., Liu Z.R. A Method of Controlling Synchronization in Diferent Systems, Chinese Physical Letters, 2003, 20(9): 1441
[251] Zhou T.S., Li C.P. Synchronization in fractional-order differential systems. Physica D: Nonlinear Phenomena, 2005,212(1): 111-125
[252] Bai E.W., Longgen K.E. Synchronization of two Lorenz systems using active control. Chaos, Solitons & Fractals, 2000,11: 1041-1044
[253] Li G.H. Generalized projective synchronization of two chaotic systems by using active control. Chaos, Solitons & Fractals, 2006, 30: 77-82
[254] Lei Y.M., Xu W., Shen J.W. Global synchronization of two parametrically excited systems using active control. Chaos, Solitons & Fractals, 2006, 28: 426-436
[255] Li G.H. An active control synchronization for two modified Chua circuits. Chinese Physics, 2005, 14(3): 472-475