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

IF 10.2 1区计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE IEEE transactions on neural networks and learning systems Pub Date : 2023-10-11 DOI:10.1109/TNNLS.2023.3321434

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

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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.

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具有时变时滞的竞争神经网络的多稳定性和鲁棒性。

本文致力于分析具有时变时滞的竞争神经网络的多稳定性和鲁棒性。从激活函数的几何结构出发，给出了确定πi=1n（2Ri+1）个平衡点共存的充分条件，其中πi=1n（Ri+1）是局部指数稳定的，其中n表示系统的一个维数，Ri是与激活函数有关的参数。导出的稳定性结果不仅包括指数稳定性，还包括幂稳定性和对数稳定性。此外，还讨论了在扰动存在的情况下，πi=1n（Ri+1）稳定平衡点的鲁棒性。与以往的文献相比，本文的结论易于验证和丰富现有的竞争神经网络的稳定性理论。最后，给出了数值算例来支持理论结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

IEEE transactions on neural networks and learning systems COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE-COMPUTER SCIENCE, HARDWARE & ARCHITECTURE

CiteScore

23.80

自引率

9.60%

发文量

2102

审稿时长

3-8 weeks

期刊介绍： The focus of IEEE Transactions on Neural Networks and Learning Systems is to present scholarly articles discussing the theory, design, and applications of neural networks as well as other learning systems. The journal primarily highlights technical and scientific research in this domain.