一类具有可变系数的混沌系统的同步  

Synchronization of chaotic systems with variable coefficients

作　　者：牛弘[1] 张国山[1] 

机构地区：[1]天津大学电气与自动化工程学院,天津300072

出　　处：《物理学报》2013年第13期105-115,共11页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:61074088)资助的课题~~

摘　　要：本文基于系统传递函数矩阵的严格正实性,针对一类具有可变系数的混沌(或超混沌)系统的自同步与异结构同步问题提出了解决方法.通过在响应系统中加入同步控制器,并将待同步系统导出的误差系统中的非线性部分作为误差系统输入,将误差状态变量作为误差系统输出,使误差系统的传递函数矩阵成为严格正实的,这样可使误差系统的原点是渐近稳定的,即两系统达到稳定的混沌(或超混沌)同步.所设计的同步控制器参数选取范围明确,均为线性的,且对于待同步系统的系数变化具有一定的鲁棒性.文中给出了同步控制器的具体设计过程和同步结果,并结合数值仿真验证了该方法的可行性与有效性.In this paper, a novel method, to synchronize two identical or different chaotic/hyperchaotic systems with variable coefficients, is proposed based on the strictly positive real transfer function matrix. By adding a synchronization controller to the response system, the nonlinear parts of the error system derived from the synchronized systems are identified as the inputs of the error system, and the error state variables are identified as the outputs of the error system. Then the transfer function matrix of the error system can be strictly positive real. As a result, the error system can be asymptotically stable at the origin, i.e., the two chaotic/hyperchaotic systems can reach stable synchronization. Moreover, the designed synchronization controllers are linear, clear in parameter selections and robust to the changes of the coefficients of the error system. The specific design processes of the synchronization controllers and the corresponding results are presented in the paper. Also, the numerical simulation results are given to verify the feasibility and effectiveness of this method.

关 键 词：严格正实 可变系数 混沌同步 

分 类 号：O415.5[理学—理论物理] O231[理学—物理]