Adaptive Synchronization Of Complex Networks With Time-varying Delays

Research of complex network is gradually penetrated into the mathematical science, life science, engineering and other fields. Dynamic analysis of complex networks has received the widespread attention. And the synchronization of networks is an important research subject. In order to describe different complex networks, a mathematical model is needed to set up, in which time delay can not be ignored. Some achievements about synchronization of complex networks with time delay are obtained, in which the time delay is generally considered to be the setting value, but the time delay is time-varying in practical application.The adaptive synchronization of coupled complex networks with time-varying delay and non delay is studied. Two networks achieve synchronization through adaptive controller. This paper also studies the generalized function projective synchronization of a class of chaotic systems with time-varying delays. Sufficient conditions are obtained for synchronization of the two complex networks.Firstly, background and research status of complex network is introduced, including some theoretical results on the synchronization. Then the purpose and significance of this paper are given. Lyapunov stability theorem, LaSalle invariant principle and several kinds of complex networks are introduced.Secondly, the adaptive synchronization between two complex networks with time-varying delays and non-delays coupling is studied. The sufficient condition is obtained to achieve synchronization. And the generalized function projective synchronization of a class of chaotic systems with time-varying delays is discussed. Two chaotic systems achieve synchronization through adaptive controller.