{"title":"Rosenzweig-Macarthur双曲切线型捕食者-猎物模型的Hopf分岔","authors":"Jing Zhang","doi":"10.22457/apam.v23n1a01808","DOIUrl":null,"url":null,"abstract":"In this paper, the Rosenzweig-MacArthur predator-prey model with the hyperbolic tangent functional response is investigated. We choose capturing efficiency of predator as the bifurcation parameter and mainly discuss the existence, direction and stability of Hopf bifurcation by Poincaré-Andronov-Hopf bifurcation theorem.","PeriodicalId":305863,"journal":{"name":"Annals of Pure and Applied Mathematics","volume":"20 1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Hopf Bifurcation of a Rosenzweig-Macarthur Hyperbolic Tangent-Type Predator-Prey Model\",\"authors\":\"Jing Zhang\",\"doi\":\"10.22457/apam.v23n1a01808\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, the Rosenzweig-MacArthur predator-prey model with the hyperbolic tangent functional response is investigated. We choose capturing efficiency of predator as the bifurcation parameter and mainly discuss the existence, direction and stability of Hopf bifurcation by Poincaré-Andronov-Hopf bifurcation theorem.\",\"PeriodicalId\":305863,\"journal\":{\"name\":\"Annals of Pure and Applied Mathematics\",\"volume\":\"20 1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Pure and Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22457/apam.v23n1a01808\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Pure and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22457/apam.v23n1a01808","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Hopf Bifurcation of a Rosenzweig-Macarthur Hyperbolic Tangent-Type Predator-Prey Model
In this paper, the Rosenzweig-MacArthur predator-prey model with the hyperbolic tangent functional response is investigated. We choose capturing efficiency of predator as the bifurcation parameter and mainly discuss the existence, direction and stability of Hopf bifurcation by Poincaré-Andronov-Hopf bifurcation theorem.
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