Stability Of Stochastic Neural Networks

New RomanNeural network has attracted the attentions of worldwide researchers for their successful applications in many fields. However,in real nervous systems,synaptic transmession is a noisy process brought on by random fluctuations from the release of neurotransmitters and other probabilistic causes,therefore,the real neural network system is a stochastic dynamic system. It is important character that we analyze stability of a stochastic dynamic system.In this thesis,we deeply investigate stability of several classes of neural networks models.It is consists of five chapters.In the first chapter,the development and history of neural networks and stochastic differential equation are briefly addressed,and the current status in stochastic neural networks is analyzed,and some notations and definitions are given in this chapter.In the second chaper,stability of stochastic Hopfield neural networks are studied. We investigate stability and instability of stochastic Hopfield neural network,some new sufficient conditions about almost sure stability and instability are established.A class of stochastic Hopfield neural network with continuously distributed delays is proposed, employing the method of stochastic analysis and inequality techniques,several sufficient conditions ensuring pth moment exponential stability are obtained.In the third chapter,stability of stochastic Recurrent neural networks(SRNN)are studied.We research stochastic Recurrent neural network with delays,by using general-ized Blythe-Liao-Mao inequality,we not only obtain almost surely exponential stability but also estimate the exponentially convergent rate.We consider robust stability of a class of stochastic Recurrent neural networks(SRNN)with time varying delays,by us-ing Razumikhin theorem,we establish some sufficient condition to determine exponential stability of SRNN.A class of hybrid stochastic Recurrent neural network(HSRNN)with time varying delays is proposed,and the mean square exponential stability of HSRNN is discussed via generalized Razumikhin theorem,some sufficient conditions are given,and by using M matrix,we obtain new criteria for the glean square exponential stability of HSRNN.In the fourth chapter,stability of stochastic Cohen-Grossberg neural networks are studied. By using the semimartingale convergence theorem,we obtain some sufficient criteria to chack the almost sure exponential stability of stochastic Cohen-Grossberg neu-ral network with time varying delays.In A class of stochastic Cohen-Grossberg neural network with unbounded distributed delays is proposed,under the help of Lyapunov func- tional and inequality, a set of novel delay-independent sufficient conditions on almost sure pth moment exponentil stability are given.In the fifth chapter, stability of stochastic fuzzy cellular neural networks are studied. We discuss stochastic fuzzy cellular neural network with delays, by constructing suitable Lyapunov functional and using Halanay inequality technique, we present some sufficient conditions ensuring almost sure exponential stability for such network. Mean square exopnential stability is investigated for stochastic delays fuzzy cellular neural networks with Markovian switching, by menas of generalized Razumikhin theorem, several sufficient conditions to ensure the mean square exponential stability of such network model are obtained.