Almost sure exponential stability of numerical solutions to stochastic delay Hopfield neural networks

Stability of numerical solutions to stochastic delay differential equations have received an increasing attention, but there has been so far little work on the stability analysis of numerical solutions to stochastic delay Hopfield neural networks. The aim of this paper is to study the almost sure exponential stability of numerical solutions to stochastic delay Hopfield neural networks by using two approaches: the Euler method and the backward Euler method. Under some reasonable conditions, both the Euler scheme and the backward Euler scheme are proved to be almost sure exponential stability. In particular, the Euler method and the backward Euler method are mainly based on the semimartingale convergence theorem.