一类带 Allee 效应的多尺度反应-扩散系统的波前解

Acta mathematica scientia,Series A ›› 2025, Vol. 45 ›› Issue (3): 776-789.

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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”

Abstract

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

CLC Number:

O175.1

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.

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

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