Multimode function multistability of Cohen-Grossberg neural networks with Gaussian activation functions and mixed time delays

Abstract

<abstract><p>This paper explores multimode function multistability of Cohen-Grossberg neural networks (CGNNs) with Gaussian activation functions and mixed time delays. We start by using the geometrical properties of Gaussian functions. The state space is partitioned into $ 3^\mu $ subspaces, where $ 0\le \mu\le n $. Moreover, through the utilization of Brouwer's fixed point theorem and contraction mapping, some sufficient conditions are acquired to ensure the existence of precisely $ 3^\mu $ equilibria for $ n $-dimensional CGNNs. Meanwhile, there are $ 2^\mu $ and $ 3^\mu-2^\mu $ multimode function stable and unstable equilibrium points, respectively. Ultimately, two illustrative examples are provided to confirm the efficacy of theoretical results.</p></abstract>