具有阿利效应和霍林 II 型功能响应的莱斯利-高尔捕食者-猎物模型的卡纳德循环和同轴轨道

IF 1.9 3区 数学 Q1 MATHEMATICS
Tianyu Shi, Zhenshu Wen
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引用次数: 0

摘要

我们研究了一个具有阿利效应和霍林第二类功能响应的快-慢莱斯利-高尔捕食者-猎物系统的动力学。更具体地说,我们提出了一些充分条件,以保证该系统存在两个正平衡点及其位置,并进一步完全确定了它们的动力学特性。基于几何奇异扰动理论和慢-快正态形式,我们确定了相关的分岔曲线,并观察到了卡纳爆炸。此外,我们还发现了一个通向鞍的慢段和快段的同轴轨道,其中,鞍的稳定流形和不稳定流形在明确的参数条件下是相连的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Canard Cycles and Homoclinic Orbit of a Leslie–Gower Predator–Prey Model with Allee Effect and Holling Type II Functional Response

Canard Cycles and Homoclinic Orbit of a Leslie–Gower Predator–Prey Model with Allee Effect and Holling Type II Functional Response

We study dynamics of a fast–slow Leslie–Gower predator–prey system with Allee effect and Holling Type II functional response. More specifically, we show some sufficient conditions to guarantee the existence of two positive equilibria of the system and their location, and then we further fully determine their dynamics. Based on geometric singular perturbation theory and the slow–fast normal form, we determine the associated bifurcation curve and observe canard explosion. Besides, we also find a homoclinic orbit to a saddle with slow and fast segments, in which, the stable and unstable manifolds of the saddle are connected under explicit parameters conditions.

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来源期刊
Qualitative Theory of Dynamical Systems
Qualitative Theory of Dynamical Systems MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
2.50
自引率
14.30%
发文量
130
期刊介绍: Qualitative Theory of Dynamical Systems (QTDS) publishes high-quality peer-reviewed research articles on the theory and applications of discrete and continuous dynamical systems. The journal addresses mathematicians as well as engineers, physicists, and other scientists who use dynamical systems as valuable research tools. The journal is not interested in numerical results, except if these illustrate theoretical results previously proved.
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