非线性耦合超混沌Rssler系统和网络的同步

Synchronization of Nonlinear Coupled Hyper-Chaotic Rssler Systems and Networks

研究两个通过非线性函数对称耦合的超混沌R ssler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R ssler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.

The synchronization of two symmetrically nonlinear-coupled hyperchaotic Roessler systems is discussed. A special nonlinear-coupled term is constructed by a suitable separation of the linear and nonlinear terms of a hyperchaotic system. The phenomenon of stable chaotic synchronization is found in a certain region around a = O. 5. The stability of the synchronous state is examined by the stability criterion of linear systems and conditional Lyapunov exponent. The synchronization of the network linked by hyperchaotic Roessler systems using special nonlinear coupling function is studied. It is shown that the stability region of coupling units is expected from an estimating stability region of two coupling units only. And the coupling strength is in inverse proportion to the number of coupling units. Numerical results demonstrate that the proposed method is effective for hyper-chaotic systems and networks.