Cluster Synchronization Of Complex Networks In Random Environment Via Decentralized Adaptive Pinning Control

Research of complex networks has been extensively penetrated in various fields such as physics, biological sciences, social sciences, computer science and engineering,economics and finance and so on, involving a lot of research contents and methods.Among these research contents, the cluster synchronization of complex networks is a crucial and interesting collective behavior. Cluster synchronization is the phenomenon which all the nodes in one cluster are synchronized and those in different clusters are not. Research on the control of cluster synchronized behavior has practical and theoretical value for modeling, analysing, designing and simulating of sub-networks.This thesis aims to investigate the cluster synchronization issue for nonlinearly coupled complex networks with non-identical dynamic systems via a specific and random pinning control strategy. This thesis is organized as follows:In the third chapter, we investigate the cluster synchronization in nonlinearly coupled complex networks of non-identical dynamic systems. We will adopt a decentralized adaptive pinning control strategy for cluster synchronization and give the negative linear adaptive feedback control to some nodes in this network.According to the nonlinear theory, the Lyapunove Stability Theorem and the Lasalle Invariance Principle, some sufficient conditions to guarantee cluster synchronization are presented. Numerical simulations by Matlab are also given to verify the theoretical results.Next, we study the cluster synchronization of nonlinearly coupled complex networks with stochastic perturbations and non-identical nodes is studied. The cluster synchronization of complex networks is achieved by designing a class of randomly occurring controller. Based on the Stability Theorem, the Stochastic Theory as well as the other theories, we obtain some criteria for cluster synchronization, and the main result generalizes the existing conclusions.Finally, we study the cluster synchronization of Markovian nonlinearly coupled complex networks with Brownian motion and time-varying delay. By designing a stochastic Lyapunov-Krasovskii function, using the Stochastic Process Theory, and giving the decentralized adaptive pinning control to some nodes in this network, the complex networks can achieve the cluster synchronization with a relatively small coupling strength. The related numerical examples are also given to confirm our theoretical results.