{"title":"Hopf Bifurcation in a Predator–Prey System with Infection","authors":"A. P. Krishchenko, O. A. Podderegin","doi":"10.1134/s00122661230110125","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We study a model of a predator–prey system with possible infection of prey in the form of\na three-dimensional system of ordinary differential equations. Using the localization method of\ncompact invariant sets, the existence of an attractor is proved and a compact positively invariant\nset is found that estimates its position. The conditions for the extinction of populations and the\nexistence of equilibria are found. A numerical method for finding a Hopf bifurcation of the inner\nequilibrium is proposed and an example of an arising stable limit cycle is given.\n</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s00122661230110125","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We study a model of a predator–prey system with possible infection of prey in the form of
a three-dimensional system of ordinary differential equations. Using the localization method of
compact invariant sets, the existence of an attractor is proved and a compact positively invariant
set is found that estimates its position. The conditions for the extinction of populations and the
existence of equilibria are found. A numerical method for finding a Hopf bifurcation of the inner
equilibrium is proposed and an example of an arising stable limit cycle is given.
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