Stability analysis of time varying delayed stochastic Hopfield neural networks in numerical simulation

This paper is concerned with the stability analysis of time varying delayed stochastic Hopfield neural networks in numerical simulation . To achieve our expected conclusions, we will reform the classical contractive mapping principle in functional analysis, with some modifications, to adapt to our conditions and both the continuous and the discrete delayed models. Under the reasonable conditions, it is shown that, the Euler-Maruyama numerical scheme is mean square exponentially stable of exact solution dependent of step size. Further more, it is also shown that the backward Euler-Maruyama numerical scheme can share the mean square exponential stability of the exact solution independent of step size under the same conditions.