Stochastic stability analysis of competitive neural networks with different time-scales

Most computational models for competitive neural networks describe activity–connectivity interactions at different time-scales. We extend these existing models by considering stochastic processes and establish stability results based on the theory of singularly perturbed stochastic systems. Based on a reduced-order model we determine conditions that ensure the existence of the exponentially mean-square stability equilibria of the stochastic nonlinear system. It is assumed that the system is described by Ito-type equations. We derive a Lyapunov function for the coupled system and an upper bound for the parameters of the independent stochastic process.