Synchronization Of Comples Dynamical Networks With Given Nonlinear Structure

With the gradually development of modern network techniques, complex networks is increasingly used to describe complex systems in real world with its characteristic of complexity. Complex dynamical networks becomes one of the hot spots, and there are several reasons. First, complex networks have broad practical backgrounds; sencond, in the reaserch of the synchronization of complex dynamical networks, the way of master stability equation is conservative and needs more improvement; third, the synchronous performance is different under the different coupled connections. So the synchronization of complex dynamical networks is worthy to study.The paper mainly investigates the synchronization of complex networks consisted of different dynamical systems and different network topology.First, general synchronization of complex network coupled with Van der Pol oscillator is studied. Based on a new circuit which simulate Van der Pol oscillator, a equation about electric current and voltage can be get, after that the equation can be exchanged to be a dynamical system. Then the network coupled with Van der Pol oscillator can be easily described by complex networks model. Finally, we can verify the feasibility of coupled circuit by Lyapunov stability theory, and then a new way of study synchronization of specific systems can be get.Second, lag synchronization for a class of complex dynamical networks coupled with Lur'e systems is studied. Due to the constraint of sector to Lur'e system, the study of this kind complex networks is highly favour, and improve its conservatism relatively. Synchronous conditions about independent-delay and dependent-delay can be got by Lyapunov stability theory.Third, cluster synchronization of complex networks which include part of mixed clusters is studied. And the mixed cluster is composed by different dynamical systems with ring connection. First, we can synchronize the community of the ring connection by some active control schemes and Lyapunov function. Then we can make the whole network achieve cluster synchronization under the condition of synchronization of the mixed cluster. At last we can verify the network we designed achieve synchronization under some synchronization conditions.