一类带 Allee 效应的多尺度反应-扩散系统的波前解

数学物理学报 ›› 2025, Vol. 45 ›› Issue (3): 776-789.

一类带 Allee 效应的多尺度反应-扩散系统的波前解

郑焰萍¹(),沈建和^1,^2,^*()

¹福建师范大学数学与统计学院福州 350117
²福建师范大学分析数学及应用教育部重点实验室, 福建省应用数学中心福州 350117

收稿日期:2024-05-08 修回日期:2024-10-05 出版日期:2025-06-26 发布日期:2025-06-20
通讯作者: *沈建和, E-mail: jhshen@fjnu.edu.cn
作者简介:郑焰萍, E-mail: 2415440857@qq.com
基金资助:
国家自然科学基金(12271096);2023年度福建省省直单位教育和科研专项项目“陆地生态系统固碳驱动的若干数学问题研究”

Traveling Fronts in a Social Tension-Outbursts Multi-Scale Reaction-Diffusion Equation with Allee Effect

Zheng Yanping¹(),Shen Jianhe^1,^2,^*()

¹School of Mathematics and Statistics, Fujian Normal University, Fuzhou 350117
²Key Laboratory of Analytical Mathematics and Applications (Ministry of Education) and Center of Applied Mathematics of Fujian Province, Fujian Normal University, Fuzhou 350117

Received:2024-05-08 Revised:2024-10-05 Online:2025-06-26 Published:2025-06-20
Supported by:
NSFC(12271096);2023 Annual Special Funding Project for Education and Research Departments in Fujian Provinces “Study on Key Mathematical Problems Driven by Carbon Seauestration in Ecosystems”

摘要/Abstract

摘要：

该文基于几何奇异摄动理论的降维方法, 结合旋转向量场和相平面分析等工具,研究了一类考虑 Allee 效应的用于描述社会张力-动荡演化多尺度反应-扩散系统的波前解的存在性. 在三种不同的极限假设下,得到了不同的降维方式并基于低维系统的异宿连接, 分别得到上述系统连接不同稳态解的波前解的存在性.

关键词: 几何奇异摄动理论, 旋转向量场, 波前解, 横截性

Abstract:

Based on the geometric singular perturbation theory, and combining with the tools of generalized rotating vector field and phase plane analysis, this paper studies the existence of traveling fronts for a class of multi-scale reaction-diffusion system describing social tension-outbursts with Allee effect. Under three different limiting assumptions on scales, we obtain three different dimension-reduction settings to get the low-dimensional systems processing heteroclinic connections. Thus, we obtain the existence of traveling fronts connecting different steady-state solutions of the multi-scale reaction-diffusion system mentioned-above.

Key words: geometric singular perturbation theory, generalized rotating vector field, traveling fronts, ttransversality

中图分类号:

O175.1

郑焰萍, 沈建和. 一类带 Allee 效应的多尺度反应-扩散系统的波前解[J]. 数学物理学报, 2025, 45(3): 776-789.

Zheng Yanping, Shen Jianhe. Traveling Fronts in a Social Tension-Outbursts Multi-Scale Reaction-Diffusion Equation with Allee Effect[J]. Acta mathematica scientia,Series A, 2025, 45(3): 776-789.

图/表 3

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