Research On Stability Of Delayed Neural Networks And Complex Network Synchronization

In order to analyze and apply easily, the transmission delays are ignored in modeling for most systems. But it is known that time delay is unavoidable. At the same time, time delays may affect the stability of the system, and even lead to instability, oscillation or chaos phenomena. Recently, research of delayed systems have attracted a large number of researchers, and many profound results have been established. The neural network, as a large-scale complex system, exhibits the rich and colorful dynamical behaviors. Due to its important and potential applications in artificial intelligence, signal processing, image processing as well as optimizing problems and so on, the dynamical issues of delayed neural networks have attracted worldwide attention in recent years, and many interesting stability criteria for the equilibriums and periodic solutions of delayed neural networks have been derived. Recently, complex networks attract more and more attentions from various fields of science and engineering. Due to the finite speeds of transmission and spreading as well as traffic congestions, a signal or influence traveling through a complex network often is associated with time delays, which is very common in biological and physical networks. So, complex dynamical networks with delays have become a focal research topic in recent years, and are attracting more and more attention from many fields of scientific research.This dissertation focuses on the global exponential and synchronous stability for several delayed system. The main achievements and originality contained in this dissertation are as follows:â‘ Global asymptotic stability for Hopfield neural networks with delaysAfter the"linearization"of the delayed Hopfield neural network model, the considered neural network model is transformed. By employing suitable Lyapunov functional, delay-dependent criteria to ensure global asymptotic stability of the equilibrium of the Hopfield neural networks are established. Our results are suitable to the general delayed Hopfield neural networks.â‘¡Global asymptotic stability for cellular neural networks with delaysThe cellular neural networks are transformed into the linear models via some equivalent transformation. By constructing a novel Lyapunov functional, sufficient criteria for the existence of a unique equilibrium and global asymptotic stability of the cellular neural network are derived. A numerical simulation is also given to illustrate the validity of our result.â‘¢Stability criteria for BAM neural networks with delaysFirst, the delayed BAM neural network model is linearized, and then, the model is parameterized transformed. Some novel delay-dependent and delay-independent asymptotical stability and exponential stability criteria for delayed BAM neural networks are derived and an estimation of the exponential convergence rate is then established by constructing an appropriate Lyapunov functional and using the linear matrix inequality (LMI) approach. Particularly, the general delayed BAM neural networks have been shifted into a class of non-autonomic linear systems under the appropriate assumption on the activation functions. The theoretical analysis and numerical simulations show that our results give some new criteria for the stability of delayed BAM neural networks.â‘£Synchronization stability criterion for complex network with coupling delaysNonlinear complex network system is transformed to linear system. A new criterion for global synchronization stability for the complex networks with coupling delays has been derived using an approach combining the Lyapunov-Krasovskii functional with LMI techniques. It has been illustrated that the proposed result generalizes and improves those reported in the literature. A numerical simulation is also given to illustrate the validity of our result.