Stability Analysis For Three Types Of Stochastic Neural Networks With Delays

Stability is a premise to ensure the normal operation of the system. Time delays,parameter uncertainty and stochastic disturbances are sources of instability oscillation andchaos phenomena of the system. So, it is necessary to research the stability of delayedstochastic neural networks, and it has profound theory significance and practical value.The stability analysis of three delayed stochastic neural networks is investigated inthis thesis based on Lyapunov stability theory and stochastic theory. Sufficient conditionsare given to ensure the stability of neural networks. Compared with some existing results,the criteria obtained in our paper are less conservative.Firstly, the stability problem for a class of stochastic neural network with discrete anddistributed delays is considered in this paper. Through constructing a novel Lyapunovfunction and some skills of disposing the matrix, under different delay conditions two newcriterions of globally asymptotic stability are derived in terms of linear matrix inequalities,which are looser than some existing and related results, and through numerical exampleand a simulation example shows the effectiveness of the conclusion.Secondly, the robust stability problem for a class of uncertain stochastic neuralnetwork with discrete and distributed delays which uncertainty is the in the form of normbounded considered in this paper. Through constructing a novel Lyapunov function, someskills of disposing the matrix and Ito 's differential equation, and then useLeibniz-Newton formula and S-procedure theorem,two new criterions of globally robustasymptotic stability are derived in terms of linear matrix inequalities,and throughnumerical example and a simulation example shows the effectiveness of the conclusion.Thirdly, the stability problem for a class of neutral-type stochastic neural networkswith time-varying delays is considered in this paper. By constructing a suitable Lyapunovfunction, using the stochastic analysis method and liberty value matrix,a new criterion ofglobally asymptotic stability are derived, which is less conservative, a numerical exampleshows the effectiveness of the conclusion.