{"title":"Existence of positive periodic solutions for a predator-prey model","authors":"C. Feng","doi":"10.5556/j.tkjm.55.2024.4821","DOIUrl":null,"url":null,"abstract":"In this paper, a class of nonlinear predator-prey models with three discrete delays is considered.\nBy linearizing the system at the positive equilibrium point and analyzing the instability of the linearized system,\ntwo sufficient conditions to guarantee the existence of positive periodic solutions of the system are obtained.\nIt is found that under suitable conditions on the parameters, time delay affects the stability of the system.\nThe present method does not need to consider a bifurcating equation which is very complex for such a predator-prey model with three discrete delays.\nSome numerical simulations are provided to illustrate our theoretical prediction.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2023-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tamkang Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5556/j.tkjm.55.2024.4821","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, a class of nonlinear predator-prey models with three discrete delays is considered.
By linearizing the system at the positive equilibrium point and analyzing the instability of the linearized system,
two sufficient conditions to guarantee the existence of positive periodic solutions of the system are obtained.
It is found that under suitable conditions on the parameters, time delay affects the stability of the system.
The present method does not need to consider a bifurcating equation which is very complex for such a predator-prey model with three discrete delays.
Some numerical simulations are provided to illustrate our theoretical prediction.
期刊介绍：
To promote research interactions between local and overseas researchers, the Department has been publishing an international mathematics journal, the Tamkang Journal of Mathematics. The journal started as a biannual journal in 1970 and is devoted to high-quality original research papers in pure and applied mathematics. In 1985 it has become a quarterly journal. The four issues are out for distribution at the end of March, June, September and December. The articles published in Tamkang Journal of Mathematics cover diverse mathematical disciplines. Submission of papers comes from all over the world. All articles are subjected to peer review from an international pool of referees.
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