Stability Criteria Analysis And Pinning Control For Discrete-time Coupled Systems

ABSTRACT:Stability and synchronization analysis of complex networks have become one of the hot spots in the present, the network connection structures are also diverse, from regular network to completely random network, among which lies the small world network and scale-free network. Different architectures result in different behaviors, the research on these behaviors can be applied to biology, finance and internet, etc.This paper is organized as follows,In the first chapter, the background knowledge has been introduced, including the research development of Rulkov model, chaos theory and the construction of small world network;The second chapter mainly focuses on the stability criteria analysis for discrete-time coupled loops with multiple delays, firstly a special polynomial is proposed, as its applications, the stability criteria of delayed coupled systems with different topological structures are established, the numerical simulation results verify the conclusions.The third chapter realizes the synchronization of discrete-time network with using pinning control, an adaptive controller is applied to the system, by constructing Lyapunov function, we prove that the controller is feasible. The numerical results show that Rulkov models undergo a complete synchronization in the coupling of small world network.The fourth chapter is a summary of this paper.