{"title":"一类时变时滞hebbian型网络的周期解问题","authors":"Mei Xu, Honghui Yin, Bo Du","doi":"10.3390/sym15111985","DOIUrl":null,"url":null,"abstract":"By using Gronwall’s inequality and coincidence degree theory, the sufficient conditions of the globally exponential stability and existence are given for a Hebbian-type network with time-varying delays. The periodic behavior phenomenon is one of the hot topics in network systems research, from which we can discover the symmetric characteristics of certain neurons. The main theorems in the present paper are illustrated using a numerical example.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Periodic Solution Problems for a Class of Hebbian-Type Networks with Time-Varying Delays\",\"authors\":\"Mei Xu, Honghui Yin, Bo Du\",\"doi\":\"10.3390/sym15111985\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"By using Gronwall’s inequality and coincidence degree theory, the sufficient conditions of the globally exponential stability and existence are given for a Hebbian-type network with time-varying delays. The periodic behavior phenomenon is one of the hot topics in network systems research, from which we can discover the symmetric characteristics of certain neurons. The main theorems in the present paper are illustrated using a numerical example.\",\"PeriodicalId\":48874,\"journal\":{\"name\":\"Symmetry-Basel\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2023-10-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Symmetry-Basel\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3390/sym15111985\",\"RegionNum\":3,\"RegionCategory\":\"综合性期刊\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MULTIDISCIPLINARY SCIENCES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Symmetry-Basel","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3390/sym15111985","RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
Periodic Solution Problems for a Class of Hebbian-Type Networks with Time-Varying Delays
By using Gronwall’s inequality and coincidence degree theory, the sufficient conditions of the globally exponential stability and existence are given for a Hebbian-type network with time-varying delays. The periodic behavior phenomenon is one of the hot topics in network systems research, from which we can discover the symmetric characteristics of certain neurons. The main theorems in the present paper are illustrated using a numerical example.
期刊介绍：
Symmetry (ISSN 2073-8994), an international and interdisciplinary scientific journal, publishes reviews, regular research papers and short notes. Our aim is to encourage scientists to publish their experimental and theoretical research in as much detail as possible. There is no restriction on the length of the papers. Full experimental and/or methodical details must be provided, so that results can be reproduced.
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