平面捕食-食饵系统奇异Hopf分岔的进一步稳定性判据。

IF 2.7 2区数学 Q1 MATHEMATICS, APPLIED

Chaos Pub Date : 2025-05-01 DOI:10.1063/5.0244624

Jicai Huang, Shimin Li, Xiaoling Wang, Kuilin Wu

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引用次数: 0

摘要

本文研究了捕食者-猎物系统的奇异Hopf分岔问题，当奇异扰动参数ε→0时特征值变为奇异时，出现了分岔。在Krupa和Szmolyan [SIAM J. Math]。分析的。（2001）]，奇异Hopf分岔的第一Lyapunov系数为L1(ε)=ε8(A+O(ε))，分岔对于A0是超临界的。就我们所知，当A=0时，关于Hopf奇异分岔的稳定性没有一般的结果。本文旨在解决平面捕食者-猎物系统的这一差距。进一步给出了Leslie型和Gause型平面捕食-食饵系统奇异Hopf分岔的稳定性判据。此外，还进行了数值模拟来支持和验证我们的分析结果。

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Further stability criteria for singular Hopf bifurcation in planar predator-prey systems.

In this paper, we investigate the singular Hopf bifurcation in predator-prey systems, where bifurcation occurs as the eigenvalues become singular when the singular perturbation parameter ε→0. In Krupa and Szmolyan [SIAM J. Math. Anal. (2001)], the first Lyapunov coefficient for singular Hopf bifurcation is given as L1(ε)=ε8(A+O(ε)), with the bifurcation being supercritical for A<0 and subcritical for A>0. As far as we know, there are no general results regarding the stability of singular Hopf bifurcation when A=0. This paper aims to address this gap for planar predator-prey systems. We present further stability criteria for singular Hopf bifurcation in planar predator-prey systems of Leslie and Gause types. Additionally, numerical simulations are conducted to support and validate our analytical findings.

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来源期刊

Chaos 物理-物理：数学物理

CiteScore

5.20

自引率

13.80%

发文量

448

审稿时长

2.3 months

期刊介绍： Chaos: An Interdisciplinary Journal of Nonlinear Science is a peer-reviewed journal devoted to increasing the understanding of nonlinear phenomena and describing the manifestations in a manner comprehensible to researchers from a broad spectrum of disciplines.