一类具有遮阳效应的植被模型的稳态分支研究

数学物理学报 ›› 2025, Vol. 45 ›› Issue (3): 875-887.

一类具有遮阳效应的植被模型的稳态分支研究

梁娟^1,^*(),郭尊光¹,张红桃²

¹太原工业学院理学系太原 030008
²中北大学数学学院太原 030051

收稿日期:2024-07-31 修回日期:2025-01-13 出版日期:2025-06-26 发布日期:2025-06-20
通讯作者: *梁娟, Email: liangjuan76@126.com
基金资助:
国家自然科学基金(42075029);山西省基础研究计划(202203021212327);山西省基础研究计划(202203021211213);太原工业学院引进人才科研资助项目(2024KJ012)

Steady-State Bifurcation for a Vegetation Model with Shading Effect

Liang Juan^1,^*(),Guo Zunguang¹,Zhang Hongtao²

¹Department of Science, Taiyuan Institute of Technology, Taiyuan 030008
²School of Mathematics, North University of China, Taiyuan 030051

Received:2024-07-31 Revised:2025-01-13 Online:2025-06-26 Published:2025-06-20
Supported by:
NSFC(42075029);Fundamental Research Program of Shanxi Province(202203021212327);Fundamental Research Program of Shanxi Province(202203021211213);Program for the (Reserved) Discipline Leaders of Taiyuan Institute of Technology(2024KJ012)

摘要/Abstract

摘要：

该文研究了一类在零流边界条件下具有遮阳效应的的植被-水反应扩散模型. 首先证明了模型的稳态分支的存在性, 并得到了稳态分支产生的条件. 其次运用Crandall-Rabinowitz 分歧定理得到了单特征值情形下非常数稳态解的结构; 运用隐函数定理和空间分解方法得到了双特征值情形下非常数稳态解的结构. 最后通过数值模拟验证了理论分析结果.}% 中文摘要

关键词: 植被模型, 稳态分支, 空间分解, 非常数解

Abstract:

A vegetation-water reaction-diffusion model with shading effect under no-flux boundary conditions is studied. The existence of steady-state bifurcation of the model is firstly proved, and the conditions for the generation of steady-state bifurcation are obtained. Then the structure of the non-constant steady-state solution in the case of single eigenvalues is obtained by using the Crandall-Rabinowitz bifurcation theorem. By adopting the implicit function theorem and the techniques of space decomposition, the structure of the non-constant steady-state solution in the case of double eigenvalues is obtained. Finally, numerical simulations are shown to verify the theoretical analysis results.

Key words: vegetation model, steady-state bifurcation, space decomposition, non-constant solutions

中图分类号:

O175

梁娟, 郭尊光, 张红桃. 一类具有遮阳效应的植被模型的稳态分支研究[J]. 数学物理学报, 2025, 45(3): 875-887.

Liang Juan, Guo Zunguang, Zhang Hongtao. Steady-State Bifurcation for a Vegetation Model with Shading Effect[J]. Acta mathematica scientia,Series A, 2025, 45(3): 875-887.

图/表 4

参考文献 15

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