{"title":"一类时滞三种共生模型的稳定性和Hopf分岔","authors":"Qin Gao","doi":"10.1109/IWCFTA.2009.63","DOIUrl":null,"url":null,"abstract":"In this paper, a three-species symbiosis Lotka–Volterra model with discrete delays is considered. The stability of positive equilibrium and the existence of Hopf bifurcations are investigated firstly and then the direction and the stability criteria of the bifurcating periodic solutions are obtained by the normal form theory and the center manifold theorem.","PeriodicalId":279256,"journal":{"name":"2009 International Workshop on Chaos-Fractals Theories and Applications","volume":"24 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2009-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Stability and Hopf Bifurcations of a Three-Species Symbiosis Model with Delays\",\"authors\":\"Qin Gao\",\"doi\":\"10.1109/IWCFTA.2009.63\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, a three-species symbiosis Lotka–Volterra model with discrete delays is considered. The stability of positive equilibrium and the existence of Hopf bifurcations are investigated firstly and then the direction and the stability criteria of the bifurcating periodic solutions are obtained by the normal form theory and the center manifold theorem.\",\"PeriodicalId\":279256,\"journal\":{\"name\":\"2009 International Workshop on Chaos-Fractals Theories and Applications\",\"volume\":\"24 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2009-11-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2009 International Workshop on Chaos-Fractals Theories and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/IWCFTA.2009.63\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2009 International Workshop on Chaos-Fractals Theories and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/IWCFTA.2009.63","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Stability and Hopf Bifurcations of a Three-Species Symbiosis Model with Delays
In this paper, a three-species symbiosis Lotka–Volterra model with discrete delays is considered. The stability of positive equilibrium and the existence of Hopf bifurcations are investigated firstly and then the direction and the stability criteria of the bifurcating periodic solutions are obtained by the normal form theory and the center manifold theorem.
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