The Stability Of Two Types Of Neural Network

This paper mainly studies on the stability of neural network dynamic systemdescribed by stochastic functional differential equations with random. Our work mainlyfocuses on two aspects. First, this paper research on the series stability of the Hopfieldmodel with discrete and distributed delays random at the same time. Second, this paperput forward a fuzzy random Cohen-Grossberg model and give the sufficient criteria ofexponential stability under the assumption based on local martingale theorem.In recent years, the distribution of time delay is introduced into the neural networkmodel. However, seldom do researchers study on model with distributed delay instochastic differential neural network, especially the p order exponential stability.Therefore this paper put forward two kinds of Hopfield neural network model withdistributed delay in Chapter3. One is the distribution with bounded time-delay modeland the other is distribution with unbounded time-delay model. For the former, it isproposed under the premise of existence solution that the model constructing Lyapunovfunction and combining techniques is proposed to be the solution of the mean squareexponential stability based on LMI inequalities. And ie has made numerical simulationto the conclusion. The advantage of LMI is that LMI can operate directly throughMatlab toolbox and it is convenient for validation. The Hopfield neural network modelwith unbounded delay distribution constructs suitable Lyapunov functions based onlocal martingale theorem of p moment and gives the adequacy of exponential stabilitycriterion. In Chapter4, this paper put forward and studied fuzzy Cohen Grossbergneural network model. To the best of our knowledge, the study for random fuzzy CohenGrossberg neural network model is less at present, and most of the researches are notconsidering random item or are just based on the fuzzy Hopfield model. This paper isbased on the fuzzy theory of Cohen Grossberg model. Inequality (LMI) technique andlocal martingale theorem are employed to reach its almost sure exponential stability oftwo parallel determine the adequacy of the conditions, which also extended some of theconclusions.