Study On Synchronization Of Complex Dynamical Networks And Chaotic Systems

Synchronization of complex dynamical networks and chaotic systems has been intensively studied in recent years, and it has become a hot topic research field of chaos. The thesis mainly focuses on the synchronization of complex dynamical networks and chaotic systems. In Chapter 1 we introduce some background knowledge and the significance of the problem we studing, and we give a brief description of research progress at the end of this chapter. In Chapter 2-6 we give some methods to realize chaotic synchronization from different points of view, corresponding mathmecical proves and numerical examples. In Chapter 2, we study the monotonous synchronization of identical Lorenz systems in complex networks, using Lorenz system's attractor and its constrictive propertity. In Chapter 3, we use impulsive method to deal with the synchronization of complex dynamical networks. In Chapter 4, we apply variational method to investigate the complete synchronization of two chaotic systems which are indirectly coupled by an intermediate system. In Chapter 5, grounded on Temam's inertia manifold theory of infinite dimensional dynamical systems, we discuss the generalized synchronization between two different systems and prove the existence of generalized synchronization manifold and its property of invariance and exponential absorption. In Chapter 6, with the help of generalized Lorenz canonical form, we study the generalized synchronization of a large group of chaotic systems. Lastly, in Chapter 7, we make a brief summary on this thesis and prospect for further research on synchronization of complex dynamical networks and chaotic systems.