耦合映射的混沌广义同步

Generalized Synchronization in Two Coupled Logistic Maps

研究了非线性耦合下两个参数不同的Ｌｏｇｉｓｔｉｃ映射的混沌广义同步问题，指出采用适当的耦合方式两个处于混沌状态的Ｌｏｇｉｓｔｉｃ映射不仅可以满足稳定的线性关系还可以满足稳定的非线性关系并给出了严格的解析证明．这是一种完全不依赖于数值计算的新方法．本文还给出了实现两个系统混沌广义同步耦合强度需取的范围以及两个系统保持稳定的线性关系和稳定的非线性关系的具体函数形式．

Interest in synchronization of chaos has increased because of its possible relevance to secure communication. Recently, papers discussing a more general idea of synchronization have appeared in the literature. We investigate chaos synchronization of nonidentical coupled maps. It is shown that two coupled Logistic maps at different parameter values may not only satisfy stable linear relation but also nonlinear relation with proper coupled fashion. The strict analytical proof about it is proposed. This is a new method that don't rely on numerical method completely. We also give the range of the coefficient of coupling in generalized synchronization and the functions of the stable linear relation and the stable nonlinear relation.