Analysis On Dynamical Behavior Of Stochastic Neural Networks With Time Delays

In this artical, the author studies the dynamical behaviors of a class of stochastic functional differential equations, which the models indicate stochastic neural networks with delays. The content contains the existence and uniquenessof the equilibrium, the stability, random passivity, well-poseness and exponential attraction in the mean square of the stochastic neural networks with delays.The main contents are as follows.First of all, the artical describesstochastic neuralnetworks with time-varying delays. Based onLyapunov stability theory, linear matrix inequality and stochastic analysis approaches, the criterionof the globally exponential stability in mean squareand the global, robust, asymptotic stability in mean square are obtained. Compared to the literature, the system is discussed the situationswhichthe status and thespeed contain time delays. The simulation experiment demonstrates the effectiveness and feasibility of the method.Secondly, the stochastic Hopfield neural networks with time delays are discused. There are anlysising the stochastic Hopfield neural networks with time-varying delays. The results of the mean square exponential stability of stochastic Hopfield neural networks are got. Compared with the traditional norm matrix estimation method, this method has less conservative.Thirdly, the problems of uncertain stochastic neural networks with leakage delay and time-varying delay are discussed, which parameters are mutually independent. By constructing appropriate Lyapunov-Krasovskii functionals, and employing Newton-Leibuniz formulation and free-weighting matrix method, the criteria for checking the random passivity of the addressed neural networks are established. The criteria which is easily checked were presented.Finally, S-distributed delays are introductedinstochastic neural network with time delays. It effectively solves the problem that discrete and distributed delays issues not included in the mutual. The existence and uniqueness of its solutionare proved. And the robustexponential stability of the system in mean square is investigated. Numerical examples demonstrate thecorrectness of the method. By using fixed points theory, the well- poseness and the exponential attraction in the mean square for stochasticneuralnetworks with S-type distributed delays are discussed. The algebraic criteria which was easily checked is presented. An example was given to show the correctnessof the conclusions. It is promoted the results of the relevant literature.