Bifurcations in a Leslie–Gower predator–prey model with strong Allee effects and constant prey refuges

IF 5.3 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Chaos Solitons & Fractals Pub Date : 2025-01-18 DOI:10.1016/j.chaos.2025.115994
Fengde Chen , Zhong Li , Qin Pan , Qun Zhu
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Abstract

In this paper, we study a Leslie–Gower predator–prey model with strong Allee effects and constant prey refuges. It is shown that the model can undergo a cusp type degenerate Bogdanov–Takens bifurcation of codimension 4, focus and elliptic types degenerate Bogdanov–Takens bifurcations of codimension 3, and degenerate Hopf bifurcation of codimension 3 as the parameters vary. The model can exhibit the coexistence of multiple positive steady states, multiple limit cycles, and homoclinic loops. Our results indicate that a larger prey refuge contributes to the coexistence of both species. Numerical simulations, including three limit cycles, quadristability, a large-amplitude limit cycle enclosing three positive steady states and a homoclinic loop, two large-amplitude limit cycles enclosing three positive steady states, are presented to illustrate the theoretical results.
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具有强Allee效应和恒定猎物避难所的Leslie-Gower捕食-食饵模型的分岔
本文研究了具有强Allee效应和恒定猎物避难所的Leslie-Gower捕食-食饵模型。结果表明,随着参数的变化,该模型可以发生余维数4的尖型简并Bogdanov-Takens分岔、余维数3的焦点型和椭圆型简并Bogdanov-Takens分岔以及余维数3的简并Hopf分岔。该模型可以表现出多个正稳态、多个极限环和同斜环的共存。我们的研究结果表明,更大的猎物避难所有助于两个物种的共存。给出了三个极限环、四次稳定性、一个大振幅极限环、三个正稳态和一个同斜环、两个大振幅极限环、三个正稳态的数值模拟来说明理论结果。
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来源期刊
Chaos Solitons & Fractals
Chaos Solitons & Fractals 物理-数学跨学科应用
CiteScore
13.20
自引率
10.30%
发文量
1087
审稿时长
9 months
期刊介绍: Chaos, Solitons & Fractals strives to establish itself as a premier journal in the interdisciplinary realm of Nonlinear Science, Non-equilibrium, and Complex Phenomena. It welcomes submissions covering a broad spectrum of topics within this field, including dynamics, non-equilibrium processes in physics, chemistry, and geophysics, complex matter and networks, mathematical models, computational biology, applications to quantum and mesoscopic phenomena, fluctuations and random processes, self-organization, and social phenomena.
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