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 $0\le \mu \le n$. 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.