一类具有恐惧效应的捕食-食饵模型的行波解

数学物理学报 ›› 2026, Vol. 46 ›› Issue (6): 2371-2386.

一类具有恐惧效应的捕食-食饵模型的行波解

张光全^*(), 汪锦馨

西安电子科技大学数学与统计学院西安 710126

收稿日期:2025-04-29 修回日期:2026-01-06 出版日期:2026-12-26 发布日期:2026-08-14
通讯作者: 张光全 E-mail:1530514696@qq.com

Traveling Wave Solutions of a Class of Predator-Prey Models with the Fear Effect

Guangquan Zhang^*(), Jingxin Wang

School of Mathematics and Statistics, Xidian University, Xi'an 710126

Received:2025-04-29 Revised:2026-01-06 Online:2026-12-26 Published:2026-08-14
Contact: Guangquan Zhang E-mail:1530514696@qq.com

摘要/Abstract

摘要：

该文研究了一类具有恐惧效应的捕食者-食饵模型的行波解的存在性与有界性. 首先, 应用 Schauder 不动点定理, 证明了该模型行波解的存在性. 随后, 通过分析方法证明了行波解的有界性, 研究表明, 当波速 $c>c^*$ 时, 模型存在有界的行波解. 所以恐惧效应在捕食者-食饵系统的种群动态中具有重要作用, 尤其是在种群的空间传播过程中更是如此. 文中的研究不仅为捕食者-食饵模型的理论研究提供了新的视角, 也为理解生态系统中恐惧效应的影响提供了理论支持.

关键词: 捕食者-食饵模型, 恐惧效应, 行波解, 种群动力学.

Abstract:

This work investigates traveling wave solutions in a predator-prey system incorporating fear effects. We establish the existence of such solutions through Schauder's fixed-point theorem and rigorously analyze their boundedness properties. The analysis reveals that bounded traveling wave solutions emerge when the wave speed exceeds a critical threshold $c^*$. These results demonstrate that fear effects significantly influence population dynamics, particularly in spatial propagation processes. The study advances the mathematical understanding of predator-prey interactions while providing a quantitative framework to assess fear-induced ecological phenomena.

Key words: predator-prey model, fear effect, traveling wave solutions, population dynamics

中图分类号:

O175.14

张光全, 汪锦馨. 一类具有恐惧效应的捕食-食饵模型的行波解[J]. 数学物理学报, 2026, 46(6): 2371-2386.

Guangquan Zhang, Jingxin Wang. Traveling Wave Solutions of a Class of Predator-Prey Models with the Fear Effect[J]. Acta mathematica scientia,Series A, 2026, 46(6): 2371-2386.

图/表 3

参考文献 14

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