Synchronization Of Complex Dynamical Systems

In recent years, synchronization of complex dynamical systems has been extensive investigated and quickly become a hot topic in the field of nonlinear dynamics. In this paper, we investigate the synchronization problem of chaotic systems and complex dynamical networks, including the following parts.The first chapter introduce the research background, theoretical approaches and related progress of chaotic systems synchronization and complex dynamical networks synchronization. The second chapter introduce some definitions and lemmas which will be used in this paper.In chapter 3, we investigate the finite time adaptive synchronization of chaotic systems, based on the stability theory of differential equations we designed a adaptive controller, then the sufficient condition for the finite-time synchronization of two chaot-ic systems is established, and the numerical simulations verified the effectiveness and feasibility of the theoretical result.In chapter 4, we investigate the generalized outer synchronization of discontinu-ous coupling complex dynamical networks, based on the stability theory of differential equations and using auxiliary system approach, we get the sufficient condition for gen-eralized outer synchronization, and the numerical simulations verified the effectiveness and feasibility of the theoretical result.In chapter 5, we study the synchronization problem of time-delayed complex dy-namical network with discontinuous coupling. Sufficient conditions for the synchro-nization are obtained based on the stability theory of differential equations. The theo-retical results show that the time-delayed networks can achieve synchronization even if the coupling is switched off sometimes. We find analytically that the speed of synchro-nization is proportional to the on-off rate of the coupling and the algebraic connectivity of networks. Finally, the analytical results are confirmed by numerical simulations.In chapter 6, the finite-time stochastic outer synchronization and generalized outer synchronization between two complex dynamical networks with time delay and noise perturbation are studied. Based on the finite-time stability theory, sufficient conditions for the finite-time outer synchronization are obtained. Numerical examples are exam-ined to illustrate the effectiveness of the analytical results. The influence of time delay and noise perturbation on the convergence time are also numerically demonstrated.In chapter 7, we make a summary of this paper and prospects for future research.