Stabilization of a generalized stochastic neural network with distributed parameters

In this paper, we study stabilization of Cohen-Grossberg type generalized neural networks with distributed parameters. The main idea is to treat the integral of the stochastic field solution to the system as the solution process to the corresponding stochastic ordinary differential equation and then discuss stabilization of the process of solution. The integral is with respect to the spatial variables. To implement this idea, we use the Itoˆ differential formula to compute the differential of a Lyapunov function along the system. The Lyapunov function is the average respect to the spatial variables. We found that there is no Itoˆ formula for the stochastic systems with distributed parameters, up to now. Our method overcomes this difficulty. Also, we have not seen any result on the stochastic neural networks with distributed parameters.