Multistability and Robustness of Competitive Neural Networks With Time-Varying Delays

Song Zhu; Jiahui Zhang; Xiaoyang Liu; Mouquan Shen; Shiping Wen; Chaoxu Mu

doi:10.1109/TNNLS.2023.3321434

Multistability and Robustness of Competitive Neural Networks With Time-Varying Delays

IEEE Trans Neural Netw Learn Syst. 2023 Oct 11:PP. doi: 10.1109/TNNLS.2023.3321434. Online ahead of print.

Authors

Song Zhu, Jiahui Zhang, Xiaoyang Liu, Mouquan Shen, Shiping Wen, Chaoxu Mu

PMID: 37819823
DOI: 10.1109/TNNLS.2023.3321434

Abstract

This article is devoted to analyzing the multistability and robustness of competitive neural networks (NNs) with time-varying delays. Based on the geometrical structure of activation functions, some sufficient conditions are proposed to ascertain the coexistence of ∏_i=1ⁿ(2R_i+1) equilibrium points, ∏_i=1ⁿ(R_i+1) of them are locally exponentially stable, where n represents a dimension of system and R_i is the parameter related to activation functions. The derived stability results not only involve exponential stability but also include power stability and logarithmical stability. In addition, the robustness of ∏_i=1ⁿ(R_i+1) stable equilibrium points is discussed in the presence of perturbations. Compared with previous papers, the conclusions proposed in this article are easy to verify and enrich the existing stability theories of competitive NNs. Finally, numerical examples are provided to support theoretical results.