Holder Continuity for Generalized SynchronizationManifolds
广义同步化流形的Holder连续性

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.