Markov Modulated Stochastic Delay Neural Network Model Of The P-order Stability

The delayed neural networks exhibiting the rich and colorful dynamical behaviors are important part of the delayed neural systems. Due to their important and potential applications in memory association, model identification as well as optimize computing and so on, the dynamical issues of delayed neural networks have attracted worldwide attention in recent years. Many extensive and in-depth researches have been made, especially in the stability of the delayed neural networks, also acquire many profound results.This thesis mainly focuses on a class stochastic neural networks with time delays and Markovian switching. Break through the limitation that take the same continuous-time Markov process with a finite number of states to model the time-delays in the excursion and diffusion, take two different but independent continuous-time Markov processes with a finite number of states Markov chains to characterize them. And then by constructing a proper Lyapunov functional, investigating the mean square stability and pth moment exponential stability of the model, obtaining a series of results, which of them improve or extend the related results in the literatures.The paper contains five chapters.Chapter 1 is the preface, which mainly introduce the research background and development of the delayed neural networks, the main problem that this papers discuss.Chapter 2 is the preliminary information, which mainly introduces the important definitions and theorems of the papers need, and then gives the detailed proof for some of these.In chapter 3, we investigate the mean square exponential stability of ordinary nonlinear continuous-time stochastic systems with time delays and Markovian switching.In chapter 4, we consider the mean stability and pth moment exponential stability of an especial SRNN model with time delays and Markovian switching.Chapter 5 is the summary and prospect, which mainly carry out the summary of the significance of the thesis, the directions and questions of the further study.