STABILITY OF NEURAL NETWORKS WITH RANDOM IMPULSES

One of the main properties of solutions of neural networks is stability and often the direct Lyapunov method is used to study stability properties. We consider the Hopfield's graded response neural network in the case when the neurons are subject to a certain impulsive state displacement at random exponentially distributed moments. It changes significantly the behavior of the solutions because they are not deterministic ones but they are stochastic processes. We examine the stability of the equilibrium of the model. Some sufficient conditions for p-moment stability of equilibrium of neural networks with time varying self-regulating parameters of all units and time varying functions of the connection between two neurons in the network are obtained. These sufficient conditions are explicitly expressed in terms of the parameters of the system and hence they are easily verifiable. We illustrate our theory on a particular nonlinear neural network.