Relaxation oscillations of a slow-fast predator-prey model with a piecewise smooth functional response

被引：15
|
作者：
Li, Shimin [1 ]
Wang, Cheng [2 ]
Wu, Kuilin [3 ]
机构：
[1] Guangdong Univ Finance & Econ, Sch Math & Stat, Guangzhou 510320, Peoples R China
[2] Nanjing Univ Finance & Econ, Sch Appl Math, Nanjing 210023, Peoples R China
[3] Guizhou Univ, Sch Math, Guiyang 550025, Peoples R China
来源：
APPLIED MATHEMATICS LETTERS | 2021年 / 113卷
基金：
中国国家自然科学基金;
关键词：
Predator-prey model; Slow-fast system; Geometric singular perturbation theory; Entry-exit function; Relaxation oscillation; SYSTEMS; STABILITY; CANARDS; CYCLES;
D O I：
10.1016/j.aml.2020.106852
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The paper investigates the relaxation oscillations of a classical predator-prey model, based on the natural ecological assumption that the maximum per capita birth rate of the predator is small in comparison with the intrinsic prey growth rate. Predator's feeding rate is assumed to be modeled by a piecewise smooth Holling type I functional response including a predator interference, which yields a piecewise smooth slow-fast system. Using geometry singular perturbation theory, we prove that the model has exactly two nested relaxation oscillations surrounding the unique stable node. Additional numerical simulations are provided to verify the analytical results. (c) 2020 Elsevier Ltd. All rights reserved.
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页数：6
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