广义混沌同步中的多稳定同步流形

从构造驱动系统和响应系统之间的函数关系出发，一般性地研究了广义混沌同步中同步流形的多值性问题，并对同步流形的稳定性进行了分析，提出了多稳定同步流形存在的条件.利用该稳定性条件对两个实例进行了分析，一个为Genesio-Rssler耦合系统，另一个为具有二次、三次非线性的耦合Duffing系统，结果表明前者仅有唯一的稳定同步流形，而后者随着耦合强度的增加，从具有两个稳定的同步流形变为只存在一个稳定同步流形. 关键词： 混沌同步 多稳定性 同步流形

Multi-stable synchronization manifold in generalized synchronization of chaos

The phenomenon of multi-stable synchronization manifold (SM) in generalized synchronization (GS) refers to the coexistence of multiple chaotic response attractors, which all synchronize with the same driving dynamics in the sense of GS. In this paper, the multivalue characteristic of SM is investigated in the general sense on the basis of establishing the functional relationship between the driving and response systems. The stability of SM is studied and the conditions ensuring the existence of the multi-stable SM are deduced. A Genesio-Rssler coupled system and a coupled Duffing system with quadric and cubic nonlinear terms are analyzed as examples and the results show that there exist only one stable SM in the former, while the bifurcation evolves from bistable SM to single-stable SM with the increase of coupling strength in the latter.