Multistability in a class of stochastic Hopfield neural networks

In this paper, the problem of multistability analysis for a class of stochastic Hopfield neural networks is considered. By utilizing the properties of activation functions and applying Schauder´s fixed-point theorem, a sufficient condition for the existence of multiple equilibria is derived. Then applying stochastic analysis technique and Lyapunov approach, a criterion is established for ensuring these equilibria to be locally exponentially stable in mean square. Estimation of positively invariant sets with probability 1 and basins of attraction for these equilibria are also obtained. Finally, an example is given to show the effectiveness of the derived results.