慢-快改进Leslie-Gower模型中的奇异分岔

IF 1.4 Q2 MATHEMATICS, APPLIED
Roberto Albarran-García , Martha Alvarez-Ramírez , Hildeberto Jardón-Kojakhmetov
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引用次数: 0

摘要

本文研究了一个具有多面手Leslie-Gower捕食者、功能性Holling II型反应和弱Allee效应的捕食-食饵系统。猎物数量的增长速度通常比捕食者快得多,这使得我们可以引入一个小的时间尺度参数来联系两个物种的增长速度,从而产生一个慢-快系统。Zhu和Liu(2022)表明,在弱Allee效应下,Hopf奇异分岔、慢速鸭式循环、弛豫振荡等。我们的主要贡献在于对一个由(简并的)跨临界分岔组织的简并情景的严格分析。采用的关键工具是爆破法,爆破法使简并奇点去具体化。此外,我们利用最新的不需要局部范式的内在技术确定了奇异Hopf分岔的临界性。理论分析得到数值分岔分析的补充,在该分岔分析中,我们在数值上识别和分析上证实了附近Takens-Bogdanov点的存在。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Singular bifurcations in a slow-fast modified Leslie-Gower model
We study a predator–prey system with a generalist Leslie–Gower predator, a functional Holling type II response, and a weak Allee effect on the prey. The prey’s population often grows much faster than its predator, allowing us to introduce a small time scale parameter ɛ that relates the growth rates of both species, giving rise to a slow-fast system. Zhu and Liu (2022) show that, in the case of the weak Allee effect, Hopf singular bifurcation, slow-fast canard cycles, relaxation oscillations, etc. Our main contribution lies in the rigorous analysis of a degenerate scenario organized by a (degenerate) transcritical bifurcation. The key tool employed is the blow-up method that desingularizes the degenerate singularity. In addition, we determine the criticality of the singular Hopf bifurcation using recent intrinsic techniques that do not require a local normal form. The theoretical analysis is complemented by a numerical bifurcation analysis, in which we numerically identify and analytically confirm the existence of a nearby Takens–Bogdanov point.
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来源期刊
Results in Applied Mathematics
Results in Applied Mathematics Mathematics-Applied Mathematics
CiteScore
3.20
自引率
10.00%
发文量
50
审稿时长
23 days
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