{"title":"Coexistence states for a class of prey–predator models with population flux by attractive transition","authors":"Sheng Xue, Shanbing Li","doi":"10.1016/j.nonrwa.2025.104321","DOIUrl":null,"url":null,"abstract":"<div><div>This paper concerns a class of prey–predator models with population flux by attractive transition under homogeneous Dirichlet boundary conditions, which is a modification of the model proposed by Kuto and Odea (Kuto and Oeda, 2022; Oeda and Kuto, 2018). We give the necessary and sufficient conditions for the existence of coexistence states. The mathematical analysis relies on an a priori estimate result and a global bifurcation method. Compared with the previous works (Kuto and Oeda, 2022; Oeda and Kuto, 2018), there are essential differences in establishing an a priori estimate result.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104321"},"PeriodicalIF":1.8000,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Real World Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1468121825000070","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
This paper concerns a class of prey–predator models with population flux by attractive transition under homogeneous Dirichlet boundary conditions, which is a modification of the model proposed by Kuto and Odea (Kuto and Oeda, 2022; Oeda and Kuto, 2018). We give the necessary and sufficient conditions for the existence of coexistence states. The mathematical analysis relies on an a priori estimate result and a global bifurcation method. Compared with the previous works (Kuto and Oeda, 2022; Oeda and Kuto, 2018), there are essential differences in establishing an a priori estimate result.
本文涉及一类猎物-捕食者模型，该模型是对Kuto和Odea提出的模型（Kuto和Oeda，2022；Oeda和Kuto，2018）的修改，在同质狄利克特边界条件下，通过吸引过渡实现种群通量。我们给出了共存状态存在的必要条件和充分条件。数学分析依赖于先验估计结果和全局分岔方法。与之前的研究（Kuto and Oeda, 2022; Oeda and Kuto, 2018）相比，在建立先验估计结果方面存在本质区别。
期刊介绍：
Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and technology such as solid and fluid mechanics, material science, mathematical biology and chemistry, control theory, and inverse problems.
The aim of Nonlinear Analysis: Real World Applications is to publish articles which are predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.
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