两类双向耦合的混沌系统的广义同步存在性  

Study on the Existence of Two Types Chaotic Generalized Synchronization of Bi-Directionally Coupled Oscillators

作　　者：过榴晓[1] 徐振源[1] 胡爱花[1] 徐训霞[1] 

机构地区：[1]江南大学理学院,江苏无锡214122

出　　处：《江南大学学报（自然科学版）》2012年第6期719-726,共8页Joural of Jiangnan University (Natural Science Edition)　

基　　金：国家自然科学基金项目(11002061;10901073)

摘　　要：针对双向耦合下两个不同混沌系统的两类广义同步流形的存在性,讨论在Y系统的修正方程具有混沌状态,同时X系统的修正系统具有渐近稳定平衡点或渐近稳定周期轨道的情况下,可将广义同步化流形存在性问题转化为Lipschitz函数族的压缩不动点,给出广义同步化流形的存在性和指数吸引性。通过双向耦合的Lorenz-Ro¨ssler混沌系统数值仿真实验证明了理论的正确及有效性。The existence of two types chaotic generalized synchronization of bi-directionally coupled different oscillators is studied. The existence of generalized synchronization can be converted to the problem of Lipschitz function family~ compression fixed point under certain conditions when the modified system of Y oscillator is chaotic, while the modified system of X oscillator collapses to a stable equilibrium or periodic oscillation. Strict theoretical proofs are given to exponential attractive property of generalized synchronization manifold. Numerical simulations on bi-directionally coupled Lorenz-R^ssler systems illustrate the correctness of the present theory.

关 键 词：双向耦合 广义同步化流形 压缩不动点 指数吸引性 

分 类 号：O415.5[理学—理论物理] O231.2[理学—物理]