Behavior of stochastic neural networks with delays

The dynamical behavior of a model for a network of neurons is analyzed. The model extends existing models for networks of neurons connected in feedback with the realistic assumptions that all neurons exhibit an unknown time delay between stimuli and response. Since the dynamical variables of interest are the firing rates of neurons, stochastic models are necessary. The stochastic stability analysis is based on the Lyapunov-Krasovskii theory for time delay systems, and yields sufficient conditions for stochastic stability independent of the delay. These are in the form of the existence of certain positive definite matrices satisfying an algebraic Riccati equation. We discuss also the probability of capture (classification) in the case of networks with several equilibria. Furthermore, it is shown that in the presence of random input perturbations an unstable network may become stable