具有收获和Holling Type I功能反应的分段光滑捕食–食饵模型的动力学分析
Dynamic Analysis of a Piecewise Smooth Predator-Prey Model with Harvesting and Holling Type I Functional Response
DOI: 10.12677/aam.2026.155203, PDF,    科研立项经费支持
作者: 刘明欢：南昌师范学院数学与信息科学学院，江西 南昌
关键词: 捕食–食饵模型；快慢系统；弛豫振荡；同宿轨；Predator-Prey Model； Fast-Slow System； Relaxation Oscillation； Homoclinic Orbit
摘要: 本文借助快慢系统相关的一些理论和概念、Fenichel理论对原系统进行了快慢分析，通过构造Poincare映射应用不动点定理等证明该具有捕食者收获和Holling Type I功能反应的分段光滑捕食–食饵模型存在弛豫振荡，同时应用隐函数定理证明同宿轨的存在性。
Abstract: In this paper, by employing theories and concepts related to fast-slow systems as well as Fenichel’s theory, we perform a fast-slow analysis on the original system. Through constructing the Poincaré map and applying the fixed point theorem, we prove the existence of relaxation oscillations in the piecewise smooth predator-prey model with predator harvesting and Holling Type I functional response. Meanwhile, the implicit function theorem is applied to establish the existence of homoclinic orbits.
文章引用：刘明欢. 具有收获和Holling Type I功能反应的分段光滑捕食–食饵模型的动力学分析[J]. 应用数学进展, 2026, 15(5): 10-17. https://doi.org/10.12677/aam.2026.155203

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