Generalized stability for discontinuous complex-valued Hopfield neural networks via differential inclusions

Abstract

Some dynamical behaviours of discontinuous complex-valued Hopfield neural networks are discussed in this paper. First, we introduce a method to construct the complex-valued set-valued mapping and define some basic definitions for discontinuous complex-valued differential equations. In addition, Leray-Schauder alternative theorem is used to analyse the equilibrium existence of the networks. Lastly, we present the dynamical behaviours, including global stability and convergence in measure for discontinuous complex-valued neural networks (CVNNs) via differential inclusions. The main contribution of this paper is that we extend previous studies on continuous CVNNs to discontinuous ones. Several simulations are given to substantiate the correction of the proposed results.