Generalized Synchronization Of Complex Dynamical Networks

This dissertation mainly studies the existence of generalized synchronization in two different chaotic continuous systems and complex dynamical networks , which consist of chaotic systems.Based on this ,the generalized synchronization is classified into several types. The sufficient criterion is rigorously proven.The author's main research work and contributions are as follows:(1) Firstly a brief introducation to historical background,research progress, conception and methods for chaos,chaotic synchronization and control ,complex dynamical networks is given.(2) Generalized synchronization of two different unidirectionally coupled chaotic Chen systems is investigated. According to the method of auxiliary-system, the theories of stability and the boundary of the responsed system, a sufficient criterion is rigorously proven. Furthermore, based on the modified system approach, GS mainflod is classified into three types.(3) The existence of Holder continuous generalized synchronization in complex networks is studied, which consist of chaotic systems. When a part of modified nodes are chaotic, and the others have asymptotically stable equilibriums or orbital asymptotically stable periodic solutions or orbital asymptotically stable periodic solutions, under certain conditions, the existence of generalized synchronization can be turned to the problem of Schauder compression fixed point in the Holder continuous space. Theoretical proofs are strictly proposed to the existence of generalized synchronization manifold.For all theoretical results,we proposed numerical simulations to illustrate the effectiveness in this dissertation.