The P-th Moment Exponential Stability Of Stochastic Neural Networks With Delays

Stochastic neural networks with delays have been the popular research topics in the nonlinear field. These kind of systems not only consider the transmission delays but also take the synaptic transmission as a noisy process. A model of stochastic neural network with delays is more convenient to express practical plant, more complex in the dynamic network behaviors and more practical in applications. In addition to the time delays and stochastic disturbances, some inevitable impulses and Markov jump parameters should be taken into account. The stability is an important character in the analysis of a stochastic dynamic system. The time delays, stochastic disturbances, impulses and Markov jump parameters may affect the stability to a large degree. In recent years, a large number of researchers have been attracted by the stability of stochastic neural networks, with a series of significant results achieved.This dissertation focuses on the study of moment exponential stability of several stochastic neural networks with delays. On the bases of stochastic Lyapunov functional theory, stochastic analysis, Razumikhin theory and Halanay inequality, some new conditions of p-th moment exponential stability for the stochastic neural networks are proposed. The concrete research contents include:(1)Stochastic recurrent neural networks with nonlinear impulses are investigated. We prove that there exists an unique equilibrium point of this system by using homomorphism. The results of moment exponential stability are obtained by stochastic analysis and inequality technique. These conditions are more applicable than some existing results.(2) Stochastic cellular neural networks are studied. By means of correct Lyapunov functional and Razumikhin theory, the results of p-th moment exponential stability of stochastic cellular neural networks with time-varying delays and impulses are obtained. We also derived some stability conditions of stochastic cellular neural networks with bounded time-varying delays and unbounded distributed delays. All these results improve and generalize some existing ones.(3) Stochastic neural networks with piecewise constant argument are concerned. It is the first time that piecewise constant arguments are introduced into stochastic neural networks. The existence and uniqueness of equilibrium point are proved by Picard iteration. Criteria on p-th moment exponential stability of equilibrium point of this system are obtained by constructing a suitable Lyapunov functional. The results of global stability of deterministic system, as a special situation of our results, are concluded in the results, and the restrictions of coefficients are found more loosen.(4)Finally, stochastic fuzzy Cohen-Grossberg neural networks with delays are discussed. By constructing suitable Lyapunov functional and using Halanay inequality, some sufficient conditions ensuring p-th moment exponential stability are proposed. P-th moment exponential stability for stochastic fuzzy Cohen-Grossberg neural networks with Markov switching are obtained also.