混沌线性广义同步新方法

两个混沌系统的广义同步是混沌全同步的一种推广。基于线性变换方法，研究混沌线性广义同步问题，提出了混沌线性广义同步新方法，该方法可以任意配置广义同步速度；给出了广义同步存在的条件；研究了两个蔡氏电路的广义同步。     

简单分段线性混沌系统与SETMOS混沌系统的自适应广义同步

研究了基于SETMOS构成的、参数未知的类双涡卷混沌系统与结构不同的简单分段线性混沌系统的广义自适应同步方法。通过分析混沌系统的特点和广义同步的定义,基于李雅普诺夫稳定性理论,提出了一种新颖的、结构简单的自适应控制器和参数更新律,来实现不同结构、驱动系统参数未知的混沌系统的广义同步。这种方法还可以应用于不同结构或相同结构的其他同步问题,如自适应广义反同步等,应用范围较广。仿真结果进一步证实了该方法的有效性和可行性。     

基于输出控制的混沌同步保密通信系统

该文提出一种基于混沌系统输出线性化的反馈控制方法,将混沌系统的非线性部分线性化,从而将复杂的非线性混沌系统的同步问题转化为简单的线性混沌系统的稳定性问题,然后通过极点配置理论,用线性化的方法同步两个非线性混沌系统。基于这种同步方法设计出混沌保密通信系统,系统的一条通道用来传输输出信号,另一条通道传输通过遮掩和调制隐藏后的信息信号。仿真结果表明这种保密通信系统是有效的。     

一类超混沌系统的广义同步研究

研究了一类四维超混沌系统的广义同步问题，基于稳定性理论得到控制器的解析表达式，分别实现了相同结构和异结构超混沌系统的广义同步，全局同步和相同步。数值计算与理论分析一致。     

新型超混沌系统同结构与异结构广义同步

基于线性系统稳定性理论,该文设计出一种新型的非线性反馈控制器,实现四维超混沌系统的同结构以及异结构的广义投影同步。该方法具有适用范围广、简单、灵活以及易于实现等优点。通过改变广义投影同步的比例因子,获得任意比例于原驱动混沌系统输出的混沌信号。数值仿真验证了所设计的控制器有效性。     

基于LMI技术的时滞混沌神经元系统的耦合延迟同步

本文研究了时滞混沌神经元系统的耦合延迟同步。运用李雅普诺夫(Lyapunov)方法和线性矩阵不等式(LMI)技术,研究了误差动力系统的渐近稳定性,获得了一些判断耦合混沌系统之间实现延迟同步的新准则。尤为重要的是,本文巧妙地将LMI形式的结论转化为广义特征值极小化问题(GEVP)来求解,并运用该方法成功地求得了耦合强度的最小值。数值实验验证了本文结论的有效性和优越性。     

超混沌复系统的自适应广义组合复同步及参数辨识

该文针对含未知参数的异结构超混沌复系统,基于自适应控制及Lyapunov稳定性理论,提出一种新的自适应广义组合复同步方法 (GCCS)。首先给出广义组合复同步的定义,将驱动-响应系统的同步问题转化为误差系统零解的稳定性问题;然后从理论上设计了非线性反馈同步控制器及参数辨识更新律,并引入误差反馈增益,以控制同步的收敛速度;最后以超混沌复Lorenz系统、超混沌复Chen系统、超混沌复L系统的广义组合复同步与参数估计为例,从数值仿真角度验证了所提方法的正确性和有效性。     

一个超混沌系统及其投影同步

 通过在Lorenz系统中加入两个控制器构造出一个五维超混沌系统,系统的超混沌特性通过Lyapunov指数得到验证,对系统的平衡点和耗散性进行了分析.基于线性系统的稳定性准则,利用线性分离方法实现了该超混沌系统的投影同步.     

基于Lyapunov方程的分数阶混沌系统投影同步

针对阶次小于1的分数阶混沌系统,结合Lyapunov方程的稳定性判定理论,实现了一类分数阶混沌系统的投影同步控制。通过该方法,保留部分了非线性项,改善混沌投影同步的性能,并从理论上证明了该方案的可行性。     

单参数统一混沌系统的自适应控制同步

研究了单参数统一混沌系统的同步问题,提出了参数自适应控制同步方法;通过构造适当的控制函数和设计参数的自适应控制律,实现了两个不同参数的统一混沌系统的同步;根据Lyapunov稳定性定理,导出了两不同参数混沌系统能实现同步的充分条件,无论驱动系统处于何种状态,该方法都可使响应系统按照驱动系统给定的轨道演化。数值仿真表明了该方法的有效性。     

基于非自治混沌系统广义同步的数字保密通信方案

在研究杜芬系统广义混沌同步的基础上,提出基于此广义混沌同步的数字保密通信的方案,将二进制信息调制为FSK信号,再由FSK信号驱动非自治混沌系统发出混沌信号,当系统处于广义混沌同步时,接收端便可恢复出二进制信息。从仿真结果看,此方案有效。     

Gain Scheduling Synchronization Method for Quadratic Chaotic Systems

A global gain scheduling synchronization method is developed in this paper for the identical synchronization of quadratic chaotic systems. The quadratic chaotic system contains nonlinearity of quadratic terms of system's states. With chaotic states being bounded in certain regions, the quadratic chaotic system can be rewritten into the linear parameter varying (LPV) form through algebraic transformations. Then, using the gain scheduling technique, two different synchronization structures are proposed to achieve the global synchronization for the quadratic chaotic system. The convergence of the synchronization errors is guaranteed under the second Lyapunov stability theory. Generalized Lorenz systems, such as the Chen system and the Lorenz system, are illustrated as examples to demonstrate the efficiency of the proposed methods.     

SYNCHRONIZATION OF CHAOTIC SYSTEMS VIA LINEAR PARTITIONS

In this paper, a new method for synchronization of chaotic systems is proposed. The method is based on the linear partitions of the chaotic system under consideration. A chaotic system is partitioned into a linear part and a nonlinear part. Under some assumptions, another chaotic system which can synchronize with the original one can be contructed. The proposed method is easier to verify and more general than the conventional one in some sense.     

基于线性状态反馈方法的Nadolschi混沌系统同步

研究了一类新型混沌系统——Nadolschi系统的同步控制问题。首先为响应系统设计一个多变量线性状态反馈控制器,进而将Nadolschi系统的同步控制问题转化为误差系统零平衡点的镇定问题。然后,根据Lyapunov稳定性理论,得出使Nadolschi混沌系统达到渐近同步的充分条件。仿真结果验证了所提方法的有效性,所设计的控制器具用结构简单,易于实现等优点。     

Generalized synchronization in networks with a complicated topology of interelement couplings

A concept of generalized synchronization is proposed. The concept is valid for both two unidirectionally or mutually coupled chaotic oscillators and networks with a complicated topology of interelement couplings and chaotic systems at the nodes. It is shown that the threshold of generalized synchronization formation in systems with 1.5 degrees of freedom can be diagnosed from the instant when the second (positive) Lyapunov exponent enters the domain of negative values. The results obtained are confirmed with the help of the nearest neighbor method. Physical mechanisms of generalized synchronization formation in such systems are revealed.     

A Design of Observers for a Discrete Chaotic System

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简化Lorenz混沌系统的投影同步控制

针对最新研究的简化Lorenz混沌系统模型,分别采用比例投影同步和广义函数投影同步控制策略,研究了两个不同初值的简化Lorenz混沌系统的同步问题.基于罗斯-霍尔维兹准则和Lyapunov稳定性原理,推导了实现两混沌系统投影同步的同步定理,确定了实现投影同步的控制参数的取值范围:分析了控制参数对同步系统性能的影响规律....     

Secure Communication via Synchronization of Lur’e Systems Using Sampled-Data Controller

In this paper, synchronization of chaotic Lur’e systems using sampled-data control is applied to the secure communication problem. The message is transmitted and masked by the techniques of n-cipher and a public key obtained by the chaotic Lur’e system. The decryption of the transmitted encrypted message to recover the original message at the receiver can be achieved by synchronizing the transmitter and receiver chaotic systems. Sampled-data feedback control is used for synchronization, and a sufficient condition for obtaining feedback gain is derived in terms of linear matrix inequalities using a discontinuous Lyapunov functional. The secure communication system is simulated via Matlab along with the Chua system to show the effectiveness of the proposed result.     

Global Asymptotical Synchronization of Chaotic Lur'e Systems Using Sampled Data: A Linear Matrix Inequality Approach

Sampled-data feedback control for master-slave synchronization schemes that consist of identical chaotic Lur'e systems is studied. Sufficient conditions for global asymptotic synchronization of such chaotic Lur'e systems are obtained using the free-weighting matrix approach and expressed in terms of linear matrix inequalities (LMIs). With the help of the LMI solvers, the sampled-data feedback control law can easily be obtained to globally asymptotically synchronize Lur'e chaotic systems. The effectiveness of the proposed method is finally illustrated via numerical simulations of chaotic Chua's circuits.