Cyclicity of slow-fast cycles with two canard mechanisms

被引：2

作者：

Yao, Jinhui ^{[1
]}

Huang, Jicai ^{[1
]}

Huzak, Renato ^{[2
]}

机构：

[1] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China

[2] Hasselt Univ, Dept Math & Stat, Campus Diepenbeek,Agoralaan Gebouw D, B-3590 Diepenbeek, Belgium

来源：

CHAOS | 2024年 / 34卷 / 05期

基金：

中国国家自然科学基金;

关键词：

MODIFIED LESLIE-GOWER; SINGULAR PERTURBATION-THEORY; PREDATOR-PREY SYSTEMS; SMOOTHNESS; MANIFOLDS; STABILITY; DELAY; MODEL;

D O I：

10.1063/5.0201887

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the cyclicity of some degenerate slow-fast cycles with two canard mechanisms in planar slow-fast systems. One canard mechanism originates from a slow-fast Hopf point and the other from a point of self-intersection where the so-called entry-exit relation can be used. By studying the difference map, we show that the cyclicity of such slow-fast cycles is at most two (the associated slow divergence integral is nonzero or vanishes). As an example, we apply this result to the modified Holling-Tanner model.

引用

页数：11

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