@article{Ke2024, 
author = {Jiang-Wei Ke and Jin-E Zhang and Ji-Xiang Zhang},
title = {Multimode function multistability of Cohen-Grossberg neural networks with Gaussian activation functions and mixed time delays},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {2},
pages = {4562-4586},
keywords = {Cohen-Grossberg neural networks, multistability, Gaussian activation functions, mixed time delays, multimode function stability},
url = {https://www.sciopen.com/article/10.3934/math.2024220},
doi = {10.3934/math.2024220},
abstract = {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    μ   subspaces, where    0  ≤  μ  ≤  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    μ   equilibria for    n-dimensional CGNNs. Meanwhile, there are        2    μ   and        3    μ    −      2    μ   multimode function stable and unstable equilibrium points, respectively. Ultimately, two illustrative examples are provided to confirm the efficacy of theoretical results.}
}