Synchronization Of Several Chaotic Systems

In recent years,chaotic synchronization has been extensive investigated and quickly become a hot topic.This dissertation considers a class of discontinuous chaotic system,a class of complex dynamical networks with time delay and random interference,fractional order Lorenz's system.The main contents of this paper are as follows:First,this paper studies a class of discontinuous chaotic system.Through the im-pulsive control and feedback control method,we obtain a sufficient condition on which discontinuous chaotic system is stabilized to the equilibrium point,At the same time,considering the synchronization problems of two discontinuous chaotic systems,we get the related stability theory and finally use numerical simulation to test the effectiveness of the proposed scheme.Second,the problem of adaptive synchronization of complex dynamical networks with time delay and random interference is investigated.Based on Lyapunov stability theorem,sufficient conditions for adaptive synchronization are obtained through rigorous mathematical proofs and the effectiveness of the result is verified by numerical simulations.Third,impulsive synchronization of fractional order Lorenz's system is investigated.The key idea is converting a fractional order system into an integer order system.Sufficient conditions for achieving stability in integer order impulsive system are derived by using Lyapunov stability theory.In particular,the scheme is simple and intuitive.Numerical simulations are given to demonstrate the feasibility and effectiveness of the proposed scheme.