Global Lagrange stability analysis of retarded SICNNs

Abstract

Abstract The stability in the Lagrange sense for cellular neural networks (CNNs) has proven to be one of the effective tools to study multi-stable dynamics of the neural networks. In this article, rather than studying the existence and Lyapunov stability of an equilibrium point we investigate multi-stable dynamics of shunting inhibitory cellular neural networks (SICNNs) with time-varying delays and coefficients. This is the first paper that addresses the Lagrange stability for SICNNs. By constructing proper Lyapunov functions and using inequality techniques, we analyze three different types of activation functions, namely, bounded, sigmoid and Lipschitz-like type activation functions. New delay-dependent sufficient criteria are derived to ensure the global Lagrange stability for SICNNs. Furthermore, globally exponentially attractive sets are given for the different activation functions. Finally, an illustrating example with numerical simulations is given to support the theoretical results.