{"title":"Effects of Random Diffusion and Advection on a Predator–Prey Model","authors":"Yu-Xia Wang, Peng-Xiang Zhang","doi":"10.1002/mma.70799","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>In this article, we investigate the steady state problem of a predator–prey model incorporating random diffusion and advection under homogeneous Dirichlet boundary conditions. To gain a better understanding of random diffusion and advection, the stability of semitrivial steady state solutions, the nonexistence and existence of positive steady-state solutions are given. The results indicate that diffusion has a significant influence on both the stability of semitrivial steady state solutions and the coexistence region. In particular, a small positive advection coefficient reduces the size of the coexistence region, whereas a large positive advection coefficient may lead to bistable phenomena. Moreover, as other parameters vary, the stability of one semitrivial steady state solution may change at least twice.</p>\n </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 13","pages":"14432-14456"},"PeriodicalIF":2.0000,"publicationDate":"2026-08-09","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.70799","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2026/5/14 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this article, we investigate the steady state problem of a predator–prey model incorporating random diffusion and advection under homogeneous Dirichlet boundary conditions. To gain a better understanding of random diffusion and advection, the stability of semitrivial steady state solutions, the nonexistence and existence of positive steady-state solutions are given. The results indicate that diffusion has a significant influence on both the stability of semitrivial steady state solutions and the coexistence region. In particular, a small positive advection coefficient reduces the size of the coexistence region, whereas a large positive advection coefficient may lead to bistable phenomena. Moreover, as other parameters vary, the stability of one semitrivial steady state solution may change at least twice.
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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