{"title":"Dynamics of a size-structured predator–prey model with chemotaxis mechanism","authors":"Xuan Tian , Shangjiang Guo","doi":"10.1016/j.nonrwa.2024.104218","DOIUrl":null,"url":null,"abstract":"<div><p>This paper is concerned with a size-structured diffusive predator–prey model with chemotaxis mechanism. The existence, linearized stability and monotonicity with respect to the growth rates of boundary steady-state solutions are analyzed. Moreover, the global stability of trivial steady-state solution under certain conditions is proved by constructing Lyapunov functional. We investigate the local and global bifurcations of positive steady-state solutions that emanate from semi-trivial steady-state solutions using Lyapunov–Schmidt reduction and bifurcation techniques when the fertility intensity of a predator or prey is used as a bifurcation parameter. It is shown that the nonlinear nonlocal chemotaxis term can lead to the emergence of Allee effect.</p></div>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1468121824001573","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: 0
Abstract
This paper is concerned with a size-structured diffusive predator–prey model with chemotaxis mechanism. The existence, linearized stability and monotonicity with respect to the growth rates of boundary steady-state solutions are analyzed. Moreover, the global stability of trivial steady-state solution under certain conditions is proved by constructing Lyapunov functional. We investigate the local and global bifurcations of positive steady-state solutions that emanate from semi-trivial steady-state solutions using Lyapunov–Schmidt reduction and bifurcation techniques when the fertility intensity of a predator or prey is used as a bifurcation parameter. It is shown that the nonlinear nonlocal chemotaxis term can lead to the emergence of Allee effect.
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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