Research On Several Kinds Of Complex Networks Synchronization Strategies And Stability Analysis

We live in all kinds of complex networks, such as neural networks, communication networks, power networks and the social networks. The study of these complex networks has more than a decade history, and has made some remarkable results. Complex network is considered as one of the advanced research topics in the twenty-first Century. At the same time, the research on the synchronization of the complex network dynamics has become an important research topic in the control engineering field. In this paper, we study the synchronization control problem of complex networks. Because the memristive neural networks as a special case of complex networks can simulate the function of human brain better, so it has aroused the enthusiasm of complex network community recently. In this paper, we have studied the complx networks with stochastic perturbations, the multi-links complex networks and the memristive neural networks. Then we get several kinds of complex network synchronization strategies and have done stability analysis. The contributions are listed in the following:(1) If a system contains nonlinearities, we usually use the method of linear approximation. But it can not control the system adequately. There is an opportunity to use the nonlinear control method to improve it. So we proposed a new adaptive nonlinear controller in order to achieve the stochastic synchronization of complex networks.(2) We propose a adaptive composite nonlinear feedback controller in order to achieve the stochastic synchronization of complex networks. It consists of an adaptive linear feedback control part and an adaptive nonlinear feedback control part. Not only can it get quickly convergent speed, but also high control precision.(3) We propose a stochastic synchronization control criteria of interdependent two-layer complex networks. We can see that both the physical layer and the cyber layer of Cyber physical systems are complex networks, and the two-layer networks are interdependent. Then we propose the mathematical model of the interdependent CPSs with stochastic perturbations, which both exist in the physical layer networks and the cyber layer networks. In addition, we study the synchronization problem of the interdependent CPSs with stochastic perturbations, and a novel adaptive nonlinear controller is proposed.(4) We get a finite time function projective synchronization criteria of multi-links complex networks. The drive system and the response system not only can get synchronization in a finite time, but also they have a complex function relationship.(5) We propose the models of memristive neural networks with impulsive perturbations, boundary perturbations or stochastic perturbations, respectively. We analysis it employs the differential inclusions theory, the stochastic differential inclusions theory and the Lyapunov functional method. Then we get some synchronization criteria and anti-synchronization criteria.(6) We propose the models of memristive neural networks with multiple proportional delays, mixed time-varying delays and the neutral-type delays, respectively. Then the randomly occurring controllers are designed to get anti-synchronization.