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

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 <= mu <= 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.