{"title":"用不动点理论研究一类具有比例时延和脉冲的复值BAM神经网络的稳定性","authors":"Min Luo , Mei Xiong , Longwei Chen , Yimin Yu","doi":"10.1016/j.rico.2025.100612","DOIUrl":null,"url":null,"abstract":"<div><div>This paper mainly studies the stability of a class of proportional delay complex-valued BAM neural networks. Using the Banach fixed-point theorem, we obtain that the equilibrium points of the neural network exist uniquely, and at the same time, we also obtain its global exponential stability. Different from previous studies, we consider neural network systems in the complex number domain. Thus, the conclusions obtained have broader applicability. Finally, we present a numerical example to verify the validity of the result.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"21 ","pages":"Article 100612"},"PeriodicalIF":3.2000,"publicationDate":"2025-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Stability of a class of complex-valued BAM neural networks with proportional delays and impulse via fixed point theory\",\"authors\":\"Min Luo , Mei Xiong , Longwei Chen , Yimin Yu\",\"doi\":\"10.1016/j.rico.2025.100612\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>This paper mainly studies the stability of a class of proportional delay complex-valued BAM neural networks. Using the Banach fixed-point theorem, we obtain that the equilibrium points of the neural network exist uniquely, and at the same time, we also obtain its global exponential stability. Different from previous studies, we consider neural network systems in the complex number domain. Thus, the conclusions obtained have broader applicability. Finally, we present a numerical example to verify the validity of the result.</div></div>\",\"PeriodicalId\":34733,\"journal\":{\"name\":\"Results in Control and Optimization\",\"volume\":\"21 \",\"pages\":\"Article 100612\"},\"PeriodicalIF\":3.2000,\"publicationDate\":\"2025-09-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Results in Control and Optimization\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2666720725000979\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Results in Control and Optimization","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2666720725000979","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
Stability of a class of complex-valued BAM neural networks with proportional delays and impulse via fixed point theory
This paper mainly studies the stability of a class of proportional delay complex-valued BAM neural networks. Using the Banach fixed-point theorem, we obtain that the equilibrium points of the neural network exist uniquely, and at the same time, we also obtain its global exponential stability. Different from previous studies, we consider neural network systems in the complex number domain. Thus, the conclusions obtained have broader applicability. Finally, we present a numerical example to verify the validity of the result.