时滞混沌系统的同步研究及电路仿真
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摘要
时滞混沌系统是一种无穷维系统,它可以产生结构相对简单,但含有多个正Lyapunov指数的超混沌系统,该系统具有极高随机性和不可预测性的时间序列,使之在安全通信中拥有广阔的应用前景。混沌同步是控制混沌实现安全通信的关键技术之一。然而,针对同步及应用的研究大都局限于理论方法分析,而系统的仿真研究仍处于起步阶段,这样就使得混沌理论研究仍然与实际工程应用之间存在着一定的距离。本文以时滞混沌系统为研究对象,开展了以下方面的研究:
(1)探讨了将时滞引入到已知的混沌系统构造出一个新的时滞系统的方法。运用控制系统原理中的Routh稳定性判据理论,判别时滞依赖混沌系统的平衡点稳定性,并在确定系统参数条件下分析了系统在平衡点处的稳定性。
(2)利用现代控制技术,研究了时滞系统的混沌同步方案。通过Lyapunov-krasovskii泛函方法推算出混沌状态轨道达到渐近稳定的条件,并进行了数值仿真验证。在同步应用中,将时滞混沌同步应用到音频保密通信中,实验证明音频信号在混沌遮掩下没有受到噪声的有效攻击,该保密通信方法具有较好的抗干扰性。
(3)为了增强非线性系统的混沌行为,运用电子工作平台Multisim软件,对改进型时滞Lorenz混沌系统的振荡器电路进行了仿真实验。设计的电路证实时滞混沌系统确实存在于自然界中,其输出波形和相图具有明显的混沌特征。
(4)设计一定的耦合比例系数,实现了时滞混沌驱动系统和响应系统的耦合同步控制的方法。并研究了混沌同步控制电路,使两个性质相同的时滞四维Lorenz系统能够实现完全同步,这在电路仿真实验中得以验证。
本文构造的两类时滞混沌同步系统能够达到满意的同步效果。设计的时滞混沌电路强化了非线性系统的混沌行为,可以作为一个高维混沌发生器,在保密通信和图像加密中具有潜在的应用价值。混沌控制电路仿真证实了文中提出的混沌耦合同步方案的有效性,并且可以按照实际需要的耦合比例实现同步控制。
Time delay chaotic system is an infinite dimension system, it can be a hyperchaotic system with large numbers of positive Lyapunov exponents. This syetem can generate highly stochastic and unpredictable time series, what makes it has the great potential of application in secure communication. Chaotic synchronization is a key technology for chaotic security communication. Nevertheless, there is still a large distance between the chaotic theory and engineering application. Time-delayed chaotic systems as study object, the main contributions of the thesis are as follows:
(1)Introducing delayed time into known chaos systems to construct new time-delayed systems. Routh stability criterion in basic principles of automatic control was firstly introduced to the stability analysis of delay-dependent systems, and the analytic procedure of a chaotic system with certain parameters was presented.
(2)Using modern control technology, chaos synchronization of delayed differential equations was designed and analyzed. Sufficient conditions of asymptotical synchronization were proposed by using Lyapunov-krasovskii functional theory. At last we realized secure communication application by means of the audio signal, and the experiment had showed the the ability to resist disturbance of the design.
(3)For the sake of enhancement of chaos in nonlinear system, an electronic circuit of advanced time delay Lorenz system was designed by using Multisim. It has chaos-like behavior, and accordances with the results of simulations.
(4) Synchronous control of the driving system and response systems, matching the certain coupling coefficient based on the time-delayed systems, was realized in this paper. Then, we designed the control circuit of two high-dimensional time-delayed chaotic systems, and simulated the circuit on the simulation software Multisim.
Based on the constructed time delay chaotic system, an implementation of chaos synchronization is well proposed. The proposed circuit which enhances the chaos in nonlinear system could be used as chaos generator, and has potential applications to signal processing and communications. The control circuit simulation confirms the effectiveness of the synchronous method,and the simulation can realize the synchronous contorl according to the coupling ratio of demand.
(1)探讨了将时滞引入到已知的混沌系统构造出一个新的时滞系统的方法。运用控制系统原理中的Routh稳定性判据理论,判别时滞依赖混沌系统的平衡点稳定性,并在确定系统参数条件下分析了系统在平衡点处的稳定性。
(2)利用现代控制技术,研究了时滞系统的混沌同步方案。通过Lyapunov-krasovskii泛函方法推算出混沌状态轨道达到渐近稳定的条件,并进行了数值仿真验证。在同步应用中,将时滞混沌同步应用到音频保密通信中,实验证明音频信号在混沌遮掩下没有受到噪声的有效攻击,该保密通信方法具有较好的抗干扰性。
(3)为了增强非线性系统的混沌行为,运用电子工作平台Multisim软件,对改进型时滞Lorenz混沌系统的振荡器电路进行了仿真实验。设计的电路证实时滞混沌系统确实存在于自然界中,其输出波形和相图具有明显的混沌特征。
(4)设计一定的耦合比例系数,实现了时滞混沌驱动系统和响应系统的耦合同步控制的方法。并研究了混沌同步控制电路,使两个性质相同的时滞四维Lorenz系统能够实现完全同步,这在电路仿真实验中得以验证。
本文构造的两类时滞混沌同步系统能够达到满意的同步效果。设计的时滞混沌电路强化了非线性系统的混沌行为,可以作为一个高维混沌发生器,在保密通信和图像加密中具有潜在的应用价值。混沌控制电路仿真证实了文中提出的混沌耦合同步方案的有效性,并且可以按照实际需要的耦合比例实现同步控制。
Time delay chaotic system is an infinite dimension system, it can be a hyperchaotic system with large numbers of positive Lyapunov exponents. This syetem can generate highly stochastic and unpredictable time series, what makes it has the great potential of application in secure communication. Chaotic synchronization is a key technology for chaotic security communication. Nevertheless, there is still a large distance between the chaotic theory and engineering application. Time-delayed chaotic systems as study object, the main contributions of the thesis are as follows:
(1)Introducing delayed time into known chaos systems to construct new time-delayed systems. Routh stability criterion in basic principles of automatic control was firstly introduced to the stability analysis of delay-dependent systems, and the analytic procedure of a chaotic system with certain parameters was presented.
(2)Using modern control technology, chaos synchronization of delayed differential equations was designed and analyzed. Sufficient conditions of asymptotical synchronization were proposed by using Lyapunov-krasovskii functional theory. At last we realized secure communication application by means of the audio signal, and the experiment had showed the the ability to resist disturbance of the design.
(3)For the sake of enhancement of chaos in nonlinear system, an electronic circuit of advanced time delay Lorenz system was designed by using Multisim. It has chaos-like behavior, and accordances with the results of simulations.
(4) Synchronous control of the driving system and response systems, matching the certain coupling coefficient based on the time-delayed systems, was realized in this paper. Then, we designed the control circuit of two high-dimensional time-delayed chaotic systems, and simulated the circuit on the simulation software Multisim.
Based on the constructed time delay chaotic system, an implementation of chaos synchronization is well proposed. The proposed circuit which enhances the chaos in nonlinear system could be used as chaos generator, and has potential applications to signal processing and communications. The control circuit simulation confirms the effectiveness of the synchronous method,and the simulation can realize the synchronous contorl according to the coupling ratio of demand.
引文
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[2] E. Ott, C. Grebogi, J. Yorke. Conntrolling chaos[J]. Phys. Rev. Lett. A, 1990(64): 1196-1199
[3] L. M. Pecora, T. L. Carroll. Driving systems with chaotic signals[J]. Phys. Rev. Lett, 1990,A44(8): 2374-2383
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[5] E. N. Lorenz. Deterministic nonperiodic flow[J]. J. Atmos. Sci, 1963,20: 130-141
[6]张琪昌,王洪礼,竺致文等.分岔与混沌理论及应用[M].天津:天津大学出版社, 2005
[7]杨晓松,李清都.混沌系统与混沌电路[M].北京:科学出版社, 2007
[8] T. Y. Li, J. A. Yorke. Period three implies chaos[J]. Am. Math. Monthly, 1975,82(10): 985-992
[9] F. Takens. Detecting Strange Attractors in Turbulence[J]. Lecture Notes in Mathematics, 1981
[10]杨绍普,申永军.滞后非线性系统的分岔与奇异性[M].北京:科学出版社, 2003
[11] A. Wolf, J. B. Swift, H. L. Swinney et al. Determining Lyapunov exponents from a time series[J]. Physica, 1985,16D: 285-317
[12]马军,王春妮. Rossler超混沌的参数辨析与同步研究[J].系统仿真学报, 2005,17(12): 3028-3032
[13]高金峰,廖旎焕.一种超混沌混合保密通信方案[J].电路与系统学报, 2005,10(4): 128-130
[14] I. Belmouhoub, M. Djemai et al. Cryptography by Discrete-time Hyperchaotic Systems[J]. Conference on Decision and Control, 2003: 1902-1907
[15] R. L. Devaney. An Introduction to Chaotic Dynamical Systems[J]. Menlo Par, CA Benjamin/Cummings, 1986
[16]李志萍.一类高维混沌系统的构造、判定及其应用[D].北京科技大学, 2005
[17]邱书凯.高维和时滞混沌系统的理论研究及电路实现[D].重庆大学, 2006
[18] L. M. Pecora, T. L. Carroll. Synchronization in chaotic system[J]. Phys. Rev. Lett, 1990,64(8): 821-824
[19]刘凌,苏燕辰.新三维混沌系统及其电路仿真实验[J].物理学报, 2007,56(04): 1966-05
[20]杨永胜.非线性系统同步化、控制及电子电路仿真设计[D].大连理工大学, 2006
[21] Liangyue Cao. Practical method for determining the minimum embedding dimension of a scalar time series[J]. Physica D, 1997: 43-50
[22] M. T. Rosenstein, J. J. Collins, C. J. De Luca. A practical method for calculating largest Lyapunov exponents from small data sets[J]. Physica D, 1993,65: 117-134
[23]吕金虎.混沌时间序列分析及其应用[M].武汉:武汉大学出版社, 2002
[24]贾飞蕾,徐伟.一类参数不确定混沌系统的延迟同步[J].物理学报, 2007,56(6): 3101-3106
[25] John Argyris. An Exploration of Chaos[M]. Amsterdam: North-Holland, 1994
[26] K. Pyragas. Transmission of signals via synchronization of chaotic time-delay systems[J]. Bifurcation and Chaos, 1998,8(9): 1839-1842
[27]赖宏慧,张小红,陈宇环. Rossler超混沌系统的混沌特性分析[J].江西理工大学学报, 2007,28(4): 1-4
[28]王兴元,王明军.三种方法实现超混沌Chen系统的反同步[J].物理学报, 2007,56(12): 6843-6850
[29]刘凌.改进Lorenz混沌系统理论分析及其电路实现[D].西南交通大学, 2006
[30]卢均治.混沌系统同步及其在通信中的应用研究[D].西安电子科技大学, 2008
[31] Heiden, Walther. Existence of chaos in control system with delayed feedback[J]. Journal of DifferentialEquations, 1983,47: 273-295
[32] Grassberger, Procaccia. Dimensions and entropies of strange attractors from a fluctuating dynamics approach[J]. Physica D, 1984,13: 34-54
[33]胡寿松.自动控制原理[M].北京:科学出版社, 2005
[34]舒永录.时滞混沌系统的构造与同步及其仿真研究[D].重庆大学, 2004
[35] K. Pyragas. Continuous control of chaos by self-controlling feedback[J]. Phys. Lett. A, 1992,170: 421-428
[36] F. Victor, Dailyudenko. Lyapunov exponents for complex systems with delayed feedback[J]. Chaos, Solitons&Fracta1s. 2003,17(2-3): 473-484
[37]陈关荣,吕金虎. Lorenz系统族的动力学分析、控制与同步[M].北京:科学出版社, 2003
[38]张永刚.具时滞控制的Rossler混沌系统的分支分析[D].哈尔滨工业大学, 2006
[39] S. Ruan, J. Wei. On the zeros of transcendental functions with applications to stability of delay differential equations with two delays[J]. Dynamics of DiscreteContinuous and Impulsive Systems, 2003,10: 863-874
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