{"title":"Dynamics of two species predator-prey model with spatially nonhomogeneous diffusion strategy","authors":"Li Ma , Haihua Liang , Huatao Wang","doi":"10.1016/j.jmaa.2025.129412","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we investigate a Holling type-II predator-prey system with spatially nonhomogeneous diffusion strategy. By employing the methods of the implicit function theorem, eigenvalue theory and bifurcation theory, we analyze the stability/instability of the positive steady state and explore the existence of a Hopf bifurcation when the diffusion rate is large. Furthermore, when the driven diffusion functions <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><msup><mrow><mi>e</mi></mrow><mrow><mi>q</mi><mi>m</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></msup></math></span> and <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>≡</mo><mn>1</mn></math></span>, we detailed discuss how the parameter <em>q</em> of the density dependent diffusion <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></span> affect the occurrence of Hopf bifurcations and the values of Hopf bifurcations.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"548 2","pages":"Article 129412"},"PeriodicalIF":1.2000,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022247X25001933","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we investigate a Holling type-II predator-prey system with spatially nonhomogeneous diffusion strategy. By employing the methods of the implicit function theorem, eigenvalue theory and bifurcation theory, we analyze the stability/instability of the positive steady state and explore the existence of a Hopf bifurcation when the diffusion rate is large. Furthermore, when the driven diffusion functions and , we detailed discuss how the parameter q of the density dependent diffusion affect the occurrence of Hopf bifurcations and the values of Hopf bifurcations.
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