Investigation Of The Stability Of Two Classes Of Stochastic Neural Networks Models

The artificial neural networks system is the dynamic system with the special structure,and it has attracted the attentions of worldwide researchers for their successful applications inmany fields. Because the system is often the influence of random factors, and the actualapplication must be based on the stability of neural networks, the research of neural networksfrom the theory and the application is very important. In this thesis, we mainly study thestability of two classes of stochastic neural networks by employing Lyapunov functionalmethod, stochastic analysis technique, inequality technique, M-matrix theory andsemi-martingale convergence theory, and the obtain conclusions improve some publishedresults.In the first chapter, the development and history of neural networks are briefly addressed,and the current status in stochastic neural networks is analyzed, and the motivations andoutlines of this paper are also given in this chapter.In the second chapter, some fundamental relevant knowledge used in this paper is brieflyintroduced.In the third chapter, mean square exponential stability of stochastic Cohen-Grossbergneural networks(SCGNN) are studied，where the state variables of the model are described bystochastic nonlinear integro-differential equations. With the help of Lyapunov function,stochastic analysis technique, and inequality techniques, some novel sufficient conditions onmean square exponential stability for SCGNN are given. Furthermore, we also establish somesufficient conditions for checking exponential stability for Cohen-Grossberg neural networkswith unbounded distributed delays.Finally, in the fourth chapter, stability of reaction–diffusion recurrent neural networks(RNNS) with continuously distributed delays and stochastic influence are considered. Somenew sufficient conditions to guarantee the almost sure exponential stability and mean squareexponential stability of an equilibrium solution are obtained, respectively. Lyapunovfunctional method, M-matrix properties, some inequality technique and nonnegative semi-m-artingale convergence theorem are used in our approach. The obtain conclusions improvesome published results.