两种群空间非均匀反应扩散竞争模型的全局渐近稳定性

数学物理学报 ›› 2025, Vol. 45 ›› Issue (4): 1171-1183.

两种群空间非均匀反应扩散竞争模型的全局渐近稳定性

吕东霆()

北京大学数学科学学院北京 100871

收稿日期:2024-09-07 修回日期:2025-02-11 出版日期:2025-08-26 发布日期:2025-08-01
作者简介:E-mail: LDT@stu.pku.edu.cn

Globally Asymptotic Stability of 2-Species Reaction-Diffusion Systems of Spatially Inhomogeneous Models

Lv Dongting()

chool of Mathematical Sciences, Peking University, Beijing 100871

Received:2024-09-07 Revised:2025-02-11 Online:2025-08-26 Published:2025-08-01

摘要/Abstract

摘要：

该文讨论了两种群空间非均匀反应扩散方程组的 Neumann 问题. 当种群的反应函数关于该种群密度不单调时, 首先利用上下解方法得到两种群唯一正平衡解的存在性; 然后证明了当扩散系数足够小时, 该解是全局渐近稳定的; 最后, 通过一个具体例子的数值解验证了结论的正确性.

关键词: 空间非均匀模型, 全局渐近稳定性, 正平衡解, 反应扩散方程组

Abstract:

The paper discusses the Neumann problem for 2-species reaction-diffusion system of spatially inhomogeneous models. When the reaction function of the species is non-monotonic with respect to its population density, firstly the existence of a unique positive equilibrium solution for both species is established by virtue of the sub-super solution technique. It is also proven that the positive equilibrium solution is globally asymptotically stable when the diffusion coefficients are sufficiently small. Finally, the correctness of the conclusion is verified through numerical solutions of a specific example.

Key words: spatially inhomogeneous model, globally asymptotic stability, positive equilibrium solution, reaction-diffusion system

中图分类号:

O175.21

吕东霆. 两种群空间非均匀反应扩散竞争模型的全局渐近稳定性[J]. 数学物理学报, 2025, 45(4): 1171-1183.

Lv Dongting. Globally Asymptotic Stability of 2-Species Reaction-Diffusion Systems of Spatially Inhomogeneous Models[J]. Acta mathematica scientia,Series A, 2025, 45(4): 1171-1183.

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