广义同步化流形的Holder连续性

证明了两个不同的混沌系统线性耦合时能实现广义同步化,在一定条件下广义同步化流形是Holder连续的.采用的思想是Temam的无穷维动力系统的惯性流形理论的改进.在线性耦合下两个混沌系统具有吸收集和吸引子的基础上,通过定义在一个函数类上的映射满足Schauder不动点定理,从而得到广义同步化流形,该广义同步化流形具有不变性.又证明了存在分数维的指数吸引子,指数吸引子与广义同步流形的交集具有指数吸引性.数值仿真证实了理论的正确性.在驱动系统和响应系统外引入辅助系统,辅助系统与响应系统的完全同步化表明了驱动系统和响应系统的广义同步化.

Holder Continuity for Generalized SynchronizationManifolds

In this paper it is shown that generalized synchronizationcan occur in two non-identical unidirectional coupled dynamical systems, and that the generalized synchronization manifolds are H\"{o}lder continuous under certainconditions. The method used here comes from Temam's theory for inertial manifoldof infinite dimensional dynamical systems. Under the presumption that two linear coupled systems have attractors and thebasin of attraction, the existence of generalized synchronization manifold isattained by Schauder's fixed-point theorem. This kind of manifold has positive invariant property.It is also proved that there is an exponential attractor with a fraction dimension, and that the intersection set of a H\"{o}lder continuous inertial manifold and anexponential attractor has exponential attraction. The theoretical results areverified by numerical simulations. An auxiliary system is introduced for the synchronization of the drive system and response system. Then the drive system and response system will be generalizedsynchronous if the auxiliary system and response system can reach completesynchronization.