Existence of Coexistence States for a Strongly Coupled Cooperative Population Model With Cross-Diffusion

IF 2 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2026-10-07 Epub Date: 2026-08-09 DOI:10.1002/mma.70932

Kerui Jiang, Zhi Ling, You Zhou

引用次数: 0

Abstract

This article investigates the existence of coexistence states for a strongly coupled cooperative elliptic system with cross-diffusion, modeling two mutualistic species. By employing the method of upper and lower solutions coupled with monotone iterative techniques, we establish sharp sufficient conditions for the existence of positive coexistence states, revealing that strong interspecific cooperation and sufficiently large intrinsic growth rates can overcome the competitive exclusion induced by cross-diffusion in hostile environments. A novel transformation is introduced to handle the strongly coupled structure, and numerical simulations are provided to validate the main theoretical findings.

查看原文本刊更多论文

交叉扩散强耦合合作种群模型共存状态的存在性

本文研究了具有交叉扩散的强耦合合作椭圆系统共存状态的存在性。利用上下解与单调迭代相结合的方法，我们建立了正共存状态存在的充分条件，揭示了强的种间合作和足够大的内在增长率可以克服敌对环境中交叉扩散引起的竞争排斥。引入了一种新的变换来处理强耦合结构，并通过数值模拟验证了主要理论结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

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.