Synchronization Of Two Classes Of Coupled Systems With External Disturbances

Due to the environmental effects, external disturbances, which may be nonlinear or even unknown, are unavoidable for practical systems, which can greatly damage the realization of chaos synchronization. This thesis considers chaos synchronization and control for two classes coupled systems with external disturbances:(a) Generalized synchronization of neural networks with discontinuous activations and time delays under bounded external perturbations;(b) Coupled nonidentical complex chaotic systems with stochastic perturbations.Firstly, based on the concepts of Filippov solutions, differential inclusion, and nonsmooth analysis, generalized lag-synchronization of neural networks with discontinuous activations and nonidentical bounded external perturbations is investigated. By designing suitable adaptive controller and new Lyapunov functionals, sufficient conditions for the synchronization goal are obtained through rigorous mathematical proofs. Results of this paper are general and include the results that for neural networks with continuous activations as a special case. Numerical simulations verify the effectiveness of the theoretical results.Secondly, the problem of adaptive synchronization for coupled nonidentical chaotic systems with complex variables and stochastic perturbations is investigated. The stochastic perturbations are also different from each other. In order to overcome the effects of the difference among the nonidentical dynamical nodes and different stochastic perturbations,a special adaptive discontinuous controller is designed, and synchronize the coupled systems onto a chaotic system with complex variables. Based on Lyapunov stability theorem and stochastic theory, sufficient conditions are obtained by rigorous mathematical proofs to ensure the synchronization of network. Finally, numerical simulation are given to illustrate the correctness of the theoretical results and the effectiveness of the control methods.