{"title":"多时滞部分依赖捕食系统的Hopf分岔","authors":"Qingsong Liu, Yiping Lin","doi":"10.1080/21642583.2014.882281","DOIUrl":null,"url":null,"abstract":"In this paper, a partial dependent predator–prey system with multiple delays is investigated. By choosing τ1, τ2 and τ3 as bifurcating parameters, we show that Hopf bifurcations occur. In addition, by using theory of functional differential equation and Hassard's method, explicit algorithms for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are derived. Finally, numerical simulations are performed to support the analytical results, and the chaotic behaviors are observed.","PeriodicalId":22127,"journal":{"name":"Systems Science & Control Engineering: An Open Access Journal","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2014-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Hopf bifurcation in a partial dependent predator–prey system with multiple delays\",\"authors\":\"Qingsong Liu, Yiping Lin\",\"doi\":\"10.1080/21642583.2014.882281\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, a partial dependent predator–prey system with multiple delays is investigated. By choosing τ1, τ2 and τ3 as bifurcating parameters, we show that Hopf bifurcations occur. In addition, by using theory of functional differential equation and Hassard's method, explicit algorithms for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are derived. Finally, numerical simulations are performed to support the analytical results, and the chaotic behaviors are observed.\",\"PeriodicalId\":22127,\"journal\":{\"name\":\"Systems Science & Control Engineering: An Open Access Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-01-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Systems Science & Control Engineering: An Open Access Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/21642583.2014.882281\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Systems Science & Control Engineering: An Open Access Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/21642583.2014.882281","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Hopf bifurcation in a partial dependent predator–prey system with multiple delays
In this paper, a partial dependent predator–prey system with multiple delays is investigated. By choosing τ1, τ2 and τ3 as bifurcating parameters, we show that Hopf bifurcations occur. In addition, by using theory of functional differential equation and Hassard's method, explicit algorithms for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are derived. Finally, numerical simulations are performed to support the analytical results, and the chaotic behaviors are observed.
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