Study On The Stability Of Delayed Neural Network

The delayed neural networks exhibiting the rich and colorful dynamical behaviors are important part of the delayed neural systems. Duo to their important and potential applications in signal processing, image processing, artificial intelligence as well as optimizing problems and so on, the dynamical issues of delayed neural networks have attracted worldwide attention in recent years. Recently, many interesting stability criteria for the equilibriums and/or periodic solutions of delayed neural networks have been derived via Lyapunov-type function/functional approaches. This thesis mainly focuses on the local and global /exponential stability for several delayed neural networks. More specifically, the main contributeions are as follows:1) Harmless Delays for Globally Asymptotic Stability of Cohen-Grossberg Neural NetworksBy constructing a novel Lyapunov functional, sufficient criteria for the existence of a unique equilibrium and globally asymptotic stability of the Cohen-Grossberg neural network are derived. These criteria are all independent of the magnitudes of the delays, and so the delays under these conditions are harmless.2) Delay-dependent Asymptotic Stability of a Two-neuron System with Different Time DelaysBased on the construction of Lyapunov functionals, we obtain sufficient criteria to ensure local and global asymptotic stability of the equilibrium of the neural network. The theoretical analysis and numerical simulations show that our results have given some new criteria for delayed neural networks.3) Delay-dependent asymptotic stability for neural networks with distributed delaysBy employing suitable Lyapunov functionals, delay-dependent criteria to ensure local and global asymptotic stability of the equilibrium of the neural networks. Our results are applied to classical Hopfield neural networks with distributed delays and some novel asymptotic stability criteria are also derived4) Estimation of exponential convergence rate and exponential stability for neural networks with time-varying delaySome new criteria for exponential stability are derived and establish an estimation of the exponential convergence rate by constructing an appropriate Lyapunov functional and using the linear matrix inequality (LMI) approach. The derived results are applicable to...