{"title":"Spatially nonhomogeneous patterns for a modified Leslie–Gower model with predator-taxis","authors":"Caijuan Jia, Yan Meng, Jiaxin Xiao","doi":"10.1016/j.cam.2025.116542","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we investigate a modified Leslie–Gower predator–prey model with predator-taxis under the Neumann boundary condition. Firstly, the boundness of solution and the global stability conditions of the positive equilibrium are performed. Secondly, we take predator-taxis sensitivity coefficient as a potential bifurcation parameter for Turing bifurcation and analyze multiple steady-state bifurcation thresholds. Then, we use weak nonlinear analysis to derive amplitude equations to determine the direction of Turing bifurcation on multiple time scales. Finally, numerical simulations check the theoretical analysis results well. It is found that the predator-taxis can induce the occurrence of nonhomogeneous steady-state solution in space.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"464 ","pages":"Article 116542"},"PeriodicalIF":2.1000,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational and Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0377042725000573","RegionNum":2,"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 investigate a modified Leslie–Gower predator–prey model with predator-taxis under the Neumann boundary condition. Firstly, the boundness of solution and the global stability conditions of the positive equilibrium are performed. Secondly, we take predator-taxis sensitivity coefficient as a potential bifurcation parameter for Turing bifurcation and analyze multiple steady-state bifurcation thresholds. Then, we use weak nonlinear analysis to derive amplitude equations to determine the direction of Turing bifurcation on multiple time scales. Finally, numerical simulations check the theoretical analysis results well. It is found that the predator-taxis can induce the occurrence of nonhomogeneous steady-state solution in space.
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The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest.
The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.
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