{"title":"Asymptotic analysis of an age-structured predator-prey model with ratio-dependent Holling Ⅲ functional response and delays","authors":"Dongxue Yan, Yuan Yuan, Xianlong Fu","doi":"10.3934/eect.2022034","DOIUrl":null,"url":null,"abstract":"This paper studies the dynamical behavior of a radio-dependent predator-prey model with age structure and two delays. The model is first formulated as an abstract non-densely defined Cauchy problem and the conditions for existence of the positive equilibrium point are derived. Then, through determining the distribution of eigenvalues, the globally asymptotic stability of the boundary equilibrium and the locally asymptotic stability for the positive equilibrium are obtained, respectively. In addition, it is also shown that a non-trivial periodic oscillation phenomenon through Hopf bifurcation appears under some conditions. Finally, some numerical examples are provided to illustrate the obtained results.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3934/eect.2022034","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 1
Abstract
This paper studies the dynamical behavior of a radio-dependent predator-prey model with age structure and two delays. The model is first formulated as an abstract non-densely defined Cauchy problem and the conditions for existence of the positive equilibrium point are derived. Then, through determining the distribution of eigenvalues, the globally asymptotic stability of the boundary equilibrium and the locally asymptotic stability for the positive equilibrium are obtained, respectively. In addition, it is also shown that a non-trivial periodic oscillation phenomenon through Hopf bifurcation appears under some conditions. Finally, some numerical examples are provided to illustrate the obtained results.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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