具有从众行为的扩散捕食者–食饵模型的入侵行波解
Invasion Traveling Waves of a Diffusive Predator-Prey Model with Herd Behavior
DOI: 10.12677/pm.2026.166162, PDF,    国家自然科学基金支持
作者: 蒲斌强, 张国宝：西北师范大学数学与统计学院，甘肃 兰州
关键词: 捕食者–食饵模型；从众行为；平方根功能响应；入侵行波解；Predator-Prey Model； Herd Behavior； Square Root Functional Response； Invasion Traveling Waves
摘要: 本文主要研究具有从众行为的扩散捕食者–食饵模型。为了刻画捕食者的入侵共存现象，我们特别关注了该模型的行波解(即入侵行波解)。通过构造一对适当的上下解并应用Schauder不动点定理，证明了超临界波速下连接边界平衡点的行波解的存在性。
Abstract: This paper focuses on the study of a diffusive predator-prey model with herd behavior. In order to characterize the invading coexistence phenomenon of predator, special attention is paid to traveling wave solutions (i.e., invasion traveling waves) of the model. By constructing a pair of suitable upper-lower solutions and applying Schauder’s fixed point theorem, we obtain the existence of traveling wave solutions with super-critical speeds and connecting the boundary equilibrium at negative infinity.
文章引用：蒲斌强, 张国宝. 具有从众行为的扩散捕食者–食饵模型的入侵行波解[J]. 理论数学, 2026, 16(6): 119-130. https://doi.org/10.12677/pm.2026.166162

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