非线性耦合超混沌R(o)ssler系统和网络的同步

研究两个通过非线性函数对称耦合的超混沌Roessler系统的同步问题．通过对超混沌系统的线性项与非线性项的适当分离,构造一个特殊的非线性函数,作为耦合函数,发现在耦合强度α=0．5附近的一小段区域里存在稳定的超混沌同步现象．利用线性系统的稳定性分析准则和条件Lyapunov指数来检验同步状态的稳定性,并进一步研究了由多个超混沌Roessler系统单元通过非线性函数按照完全连接形式组成的网络的混沌同步问题。显示许多耦合单元组成的网络,满足同步稳定性的耦合强度的取值范围可以仅从2个单元组成的网络的参数取值范围估计到。此外发现耦合强度的值与耦合单元数量成反比,数值模拟结果证实所提出方法对超混沌系统和网络的混沌同步是有效的。     

超混沌R?ssler系统构成的星形网络的混沌同步

通过对超混沌系统线性项与非线性项的适当分离配置，构造一个特殊的非线性耦合函数作为单元之间的耦合函数，提出非线性非对称耦合混沌同步方法，研究超混沌Rssler系统单元按照星形连接形式组成网络的同步问题.发现耦合强度在某一区域里存在着稳定的混沌同步现象.分析并讨论了不同参数在耦合过程中对混沌同步过程及其稳定性的影响.数值模拟结果证实该方法的有效性. 关键词： 超混沌同步 非线性耦合 R ssler系统 星形网络     

Synchronization in coupled nonidentical incommensurate fractional-order systems

Synchronization of fractional-order nonlinear systems has received considerable attention for many research activities in recent years. In this Letter, we consider the synchronization between two nonidentical fractional-order systems. Based on the open-plus-closed-loop control method, a general coupling applied to the response system is proposed for synchronizing two nonidentical incommensurate fractional-order systems. We also derive a local stability criterion for such synchronization behavior by utilizing the stability theory of linear incommensurate fractional-order differential equations. Feasibility of the proposed coupling scheme is illustrated through numerical simulations of a limit cycle system, a chaotic system and a hyperchaotic system.     

部分线性的分数阶混沌系统修正函数投影同步

针对一类部分线性的分数阶混沌系统修正函数投影同步问题, 可通过单变量耦合构造出这类系统的响应系统, 从而提出修正函数投影同步的设计方法. 根据Routh-Hurwitz条件, 给出耦合部分线性系统实现修正函数投影同步的方法, 并设计了控制器. 该方法中控制器和误差动态方程的选择都是确定的, 理论分析和数值仿真都说明了该方法在部分线性的分数阶混沌系统中应用具有可行性和有效性. 关键词： 分数阶混沌系统 部分线性 修正函数投影同步     

Reliability of linear coupling synchronization of hyperchaotic systems with unknown parameters

Complete synchronization could be reached between some chaotic and/or hyperchaotic systems under linear coupling. More generally, the conditional Lyapunov exponents are often calculated to confirm the stability of synchronization and reliability of linear controllers. In this paper, detailed proof and measurement of the reliability of linear controllers are given by constructing a Lyapunov function in the exponential form. It is confirmed that two hyperchaotic systems can reach complete synchronization when two linear controllers are imposed on the driven system unidirectionally and the unknown parameters in the driving systems are estimated completely. Finally, it gives the general guidance to reach complete synchronization under linear coupling for other chaotic and hyperchaotic systems with unknown parameters.     

分数阶混沌系统与整数阶混沌系统之间的同步

基于追踪控制的思想,利用分数阶系统稳定性理论,实现了分数阶混沌系统与整数阶混沌系统之间的混沌同步,给出了补偿器和反馈控制器的选择方法.以三维分数阶Chen系统和三维整数阶Lorenz混沌系统之间的混沌同步为例进行了数值仿真和电路仿真.研究表明了该同步方法的有效性。     

Impulsive Synchronization of Laser Plasma System

The issue of impulsive synchronization of the coupled chaotic laser plasma system is investigated. A new framework for impulsive synchronization of such chaotic systems is presented, which makes the synchronization error system a linear impulsive control system. We derive some sufficient conditions for the synchronization of a laser plasma system via impulsive control with the varying impulsive intervals, which allows us to derive the impulsive synchronization law easily. To illustrate the effectiveness of the proposed results, two numerical examples are given.     

Lag projective synchronization in fractional-order chaotic (hyperchaotic) systems

In this Letter, a new lag projective synchronization for fractional-order chaotic (hyperchaotic) systems is proposed, which includes complete synchronization, anti-synchronization, lag synchronization, generalized projective synchronization. It is shown that the slave system synchronizes the past state of the driver up to a scaling factor. A suitable controller for achieving the lag projective synchronization is designed based on the stability theory of linear fractional-order systems and the pole placement technique. Two examples are given to illustrate effectiveness of the scheme, in which the lag projective synchronizations between fractional-order chaotic Rössler system and fractional-order chaotic Lü system, between fractional-order hyperchaotic Lorenz system and fractional-order hyperchaotic Chen system, respectively, are successfully achieved. Corresponding numerical simulations are also given to verify the analytical results.     

Hybrid projective synchronization of chaotic fractional order systems with different dimensions

The hybrid projective synchronization of different dimensional fractional order chaotic systems is investigated in this paper. It is shown that the slave system can be synchronized with the projection of the master system generated through state transformation. Based on the stability theorem of linear fractional order systems, a suitable controller for achieving the synchronization is given. The hybrid projective synchronization between the fractional order chaotic system and hyperchaotic system is successfully achieved in both reduced order and increased order. The corresponding numerical results verify the effectiveness of the proposed method.     

忆阻混沌系统的脉冲同步与初值影响研究

以光滑三次型磁控忆阻器的蔡氏电路为例, 研究了两个同构忆阻混沌系统的脉冲控制同步方法.基于Lyapunov稳定性理论, 给出了忆阻混沌系统的脉冲同步渐近稳定条件; 结合误差系统的最大条件Lyapunov指数谱, 讨论了系统初值对脉冲同步性能的影响, 并进行了相应的数值仿真实验.结果表明, 在合适的脉冲控制参数条件下, 同构的忆阻混沌系统的脉冲同步是可行而有效的; 忆阻混沌系统的初值对脉冲同步性能存在一定的影响, 但可通过增大脉冲耦合强度来抑制系统初值的影响.     

声光双稳系统的混沌同步

首先给出布拉格型声光双稳系统耦合驱动的混沌同步化方案，用最大条件Ｌｙａｐｕｎｏｖ指数分析方法得出耦合驱动下系统混沌输出同步化条件，发现通过适当比例的耦合驱动可以使两组混沌系统达到同步的混沌输出。分析此混沌同步化方案可以抵抗噪声的干扰，并且在两系统出现偏差时仍可以实现混沌同步，找到了实用的单变量延时微分系统非Ｐｅｃｏｒａ－Ｃａｒｒｏｌｌ规则的混沌同步化方案。最后做了实验验证。     

基于引力场理论的混沌同步

通过引入分布引力场,将混沌系统的同步问题等效为引力场中系统运行轨道一致问题,从而实现更多不同动力学混沌系统的同步.通过将混沌系统之间的耦合度定义为速度,因其与运动方程无关,从而有别于常见的混沌同步控制项,具有较强通用性.基于轨道逼近导出引力场中多个混沌系统同步的条件,给出同步轨道方程.数值仿真实验说明了该方法的有效性.     

基于线性耦合下混沌系统的同步条件

将混沌同步问题用精确的数学语言给予描述，通过数学分析将其转化为微分方程组的稳定性问题.以Lorenz系统族的Chen氏系统作为典型系统，在线性耦合下分析系统参数，得到了系统达到同步时的充分条件，且在理论上加以证明.结合该条件，提出了一种确定耦合系数的方法.最后用仿真实验验证了该方法的正确性，并验证了在不同耦合方式和参考系统的情况下定理的有效性. 关键词： 混沌同步 耦合 稳定性     

Generalized projective synchronization of a class of fractional-order chaotic systems via a scalar transmitted signal

In this Letter, a drive-response synchronization method with linear output error feedback is presented for “generalized projective synchronization” of a class of fractional-order chaotic systems via a scalar transmitted signal. This synchronization approach is theoretically and numerically studied. By using stability theory of linear fractional-order systems, the suitable conditions for achieving synchronization are given. Two examples are used to illustrate the effectiveness of the proposed synchronization method. Numerical simulations coincide with the theoretical analysis.     

分数阶混沌系统的异结构同步

基于分数阶线性系统稳定性理论,结合反馈控制和主动控制方法,提出了一种分数阶混沌系统异结构同步方法,给出了同步控制器解析式. 以分数阶Chen混沌系统和分数阶Liu混沌系统、分数阶新超混沌系统和分数阶超混沌Rssler系统的异结构同步为例, 进行了数值模拟,证实了该方法的有效性和可行性. 关键词： 分数阶混沌 异结构混沌同步 新超混沌系统 超混沌Rssler系统     

Electronic Structure Studies of Bi2Sr2CaCu2-xSnxO8+δ System

This paper presents a linear output feedback synchronization approach for a chaotic Arneodo system. Based on the linear stability theorem, a sufficient condition of asymptotic synchronization is given, and the boundary of the range of the output feedback parameter is given also. Finally, a computer simulation is given to demonstrate the effectiveness of the method.     

Exponential networked synchronization of master-slave chaotic systems with time-varying communication topologies

The networked synchronization problem of a class of master-slave chaotic systems with time-varying communication topologies is investigated in this paper. Based on algebraic graph theory and matrix theory, a simple linear state feedback controller is designed to synchronize the master chaotic system and the slave chaotic systems with a time- varying communication topology connection. The exponential stability of the closed-loop networked synchronization error system is guaranteed by applying Lyapunov stability theory. The derived novel criteria are in the form of linear matrix inequalities (LMIs), which are easy to examine and tremendously reduce the computation burden from the feedback matrices. This paper provides an alternative networked secure communication scheme which can be extended conveniently. An illustrative example is given to demonstrate the effectiveness of the proposed networked synchronization method.     

混沌Arneodo系统的输出反馈同步

对Arneodo混沌系统进行输出线性反馈同步.基于线性稳定性定理,给出了一个同步渐近稳定的充分条件,和同步渐近稳定的反馈系数的范围.对同步系统进行数值仿真,验证了方法的有效性和抗噪声能力. 关键词：     

基于线性分离的自治混沌系统的投影同步

分析了自治混沌系统的投影同步问题.基于线性系统的稳定判定准则，提出一种新的线性分离的同步方法，并采用该方法实现了Lorenz系统，Rssler系统和超混沌Chen系统的投影同步.数值模拟进一步验证了所提出方案的有效性. 关键词： 投影同步 自治混沌系统 线性分离     

基于LMI的参数未知时变时滞混沌系统模糊自适应H_∞同步

考虑一类结构相同但驱动系统参数未知的两个时变时滞混沌系统同步问题,提出了基于T-S模糊模型的模糊自适应H∞同步方法.基于Lyapunov稳定性理论和线性矩阵不等式技术,给出了驱动系统参数未知时变时滞混沌系统同步的充分条件.仿真结果表明了所提方法的有效性.