Song Zhu, Jiahui Zhang, Xiaoyang Liu, Mouquan Shen, Shiping Wen, Chaoxu Mu
{"title":"具有时变时滞的竞争神经网络的多稳定性和鲁棒性。","authors":"Song Zhu, Jiahui Zhang, Xiaoyang Liu, Mouquan Shen, Shiping Wen, Chaoxu Mu","doi":"10.1109/TNNLS.2023.3321434","DOIUrl":null,"url":null,"abstract":"<p><p>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 ∏<sub>i=1</sub><sup>n</sup>(2R<sub>i</sub>+1) equilibrium points, ∏<sub>i=1</sub><sup>n</sup>(R<sub>i</sub>+1) of them are locally exponentially stable, where n represents a dimension of system and R<sub>i</sub> 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 ∏<sub>i=1</sub><sup>n</sup>(R<sub>i</sub>+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.</p>","PeriodicalId":13303,"journal":{"name":"IEEE transactions on neural networks and learning systems","volume":"PP ","pages":""},"PeriodicalIF":10.2000,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Multistability and Robustness of Competitive Neural Networks With Time-Varying Delays.\",\"authors\":\"Song Zhu, Jiahui Zhang, Xiaoyang Liu, Mouquan Shen, Shiping Wen, Chaoxu Mu\",\"doi\":\"10.1109/TNNLS.2023.3321434\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>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 ∏<sub>i=1</sub><sup>n</sup>(2R<sub>i</sub>+1) equilibrium points, ∏<sub>i=1</sub><sup>n</sup>(R<sub>i</sub>+1) of them are locally exponentially stable, where n represents a dimension of system and R<sub>i</sub> 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 ∏<sub>i=1</sub><sup>n</sup>(R<sub>i</sub>+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.</p>\",\"PeriodicalId\":13303,\"journal\":{\"name\":\"IEEE transactions on neural networks and learning systems\",\"volume\":\"PP \",\"pages\":\"\"},\"PeriodicalIF\":10.2000,\"publicationDate\":\"2023-10-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"IEEE transactions on neural networks and learning systems\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.1109/TNNLS.2023.3321434\",\"RegionNum\":1,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE transactions on neural networks and learning systems","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1109/TNNLS.2023.3321434","RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
Multistability and Robustness of Competitive Neural Networks With Time-Varying Delays.
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(2Ri+1) equilibrium points, ∏i=1n(Ri+1) of them are locally exponentially stable, where n represents a dimension of system and Ri 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(Ri+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.
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.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
