Graph theoretical approach for construction of Lyapunov function for a coupled stochastic neural network

Abstract

In this paper, we describe a new model of coupled stochastic neural network given by a system of stochastic functional differential equations (SFDE’s) and give a way for construction of a Lyapunov function of the system. The considered coupled system is in fact a large system of SFDEs driven by n-dimensional Brownian motion, with impulses and Markovian switching. This complex system consists of large number of interconnected, mutually interacting neural networks with their own dynamics. The considered model is more complex than the ones presented in the literature and thus it is more difficult to analyze its stability properties. We take an approach from the graph theory which will give us an elegant way to construct the Lyapunov function. The result is important since the function can be effectively used to analyze the stability properties of the coupled system.