{"title":"Bifurcation and stability analysis of a Leslie–Gower diffusion predator–prey model with prey refuge and Beddington–DeAngelis functional response","authors":"Xiaozhou Feng, Kunyu Li, Haixia Li","doi":"10.1002/mma.10470","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we consider the spatiotemporal dynamics behaviors of a Leslie–Gower diffusion predator–prey system with prey refuge and Beddington–DeAnglis (B-D) functional response. By using the Poincaré inequality and topological degree theory, we first investigate the Turing instability of the reaction–diffusion system and prove the existence of nonconstant positive steady-state solutions. Then we discuss the steady-state bifurcation and the direction to Hopf bifurcation of the PDE model by the local bifurcation theorem and center manifold theory. Finally, some numerical simulations are presented to supplement the analytic results in one dimension which indicates that changes in prey refuge and diffusion coefficient can increase the complexity of the system.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 3","pages":"2954-2979"},"PeriodicalIF":2.1000,"publicationDate":"2024-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Methods in the Applied Sciences","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mma.10470","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we consider the spatiotemporal dynamics behaviors of a Leslie–Gower diffusion predator–prey system with prey refuge and Beddington–DeAnglis (B-D) functional response. By using the Poincaré inequality and topological degree theory, we first investigate the Turing instability of the reaction–diffusion system and prove the existence of nonconstant positive steady-state solutions. Then we discuss the steady-state bifurcation and the direction to Hopf bifurcation of the PDE model by the local bifurcation theorem and center manifold theory. Finally, some numerical simulations are presented to supplement the analytic results in one dimension which indicates that changes in prey refuge and diffusion coefficient can increase the complexity of the system.
期刊介绍：
Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome.
Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted.
Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.
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