Dynamic transcritical bifurcations in a class of slow-fast predator-prey models

被引：17

作者：

Boudjellaba, Hafida ^{[2
]}

Sari, Tewfik ^{[1
]}

机构：

[1] Univ Haute Alsace, F-68093 Mulhouse, France

[2] Laurentian Univ, Sudbury, ON P3E 2C6, Canada

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2009年 / 246卷 / 06期

关键词：

Asymptotic stability; Delayed loss of stability; Singular perturbations; Canards; Biological models; ORDINARY DIFFERENTIAL-EQUATIONS; UNSTABLE PERIODIC MOTIONS; CANARDS; POPULATIONS; EXISTENCE; R-3;

D O I：

10.1016/j.jde.2009.01.001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the stability loss delay phenomenon in a dynamic transcritical bifurcation in a class of three-dimensional prey and predator systems. The dynamics of the predator is assumed to be slow comparatively to the dynamics of the prey. As an application, a well-known model considered by Clark will be discussed. (C) 2009 Elsevier Inc. All rights reserved.

引用

下载

页码：2205 / 2225

页数：21

共 50 条

[21] Observer normal forms for a class of Predator-Prey models
Boutat, D.
Saif, M.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2016, 353 (10): : 2178 - 2198
[22] Relaxation Oscillations and Dynamical Properties in a Time Delay Slow-Fast Predator-Prey Model with a Piecewise Smooth Functional Response
Qian, Youhua
Peng, Yuhui
Wang, Yufeng
Lin, Bingwen
MATHEMATICS, 2022, 10 (09)
[23] Relaxation oscillations in a slow-fast predator-prey model with weak Allee effect and Holling-IV functional response
Zhao, Liang
Shen, Jianhe
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2022, 112
[24] Complex dynamics of a discrete-time Leslie-Gower predator-prey system with herd behavior and slow-fast effect on predator population
Tahir, Naheed
Ahmed, Rizwan
Shah, Nehad Ali
INTERNATIONAL JOURNAL OF BIOMATHEMATICS, 2024,
[25] Bifurcations and Pattern Formation in a Predator-Prey Model
Cai, Yongli
Gui, Zhanji
Zhang, Xuebing
Shi, Hongbo
Wang, Weiming
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2018, 28 (11):
[26] BIFURCATIONS OF EQUILIBRIA IN BAZYKIN PREDATOR-PREY MODEL
METZLER, W
WISCHNIEWSKY, W
MATHEMATICAL MODELLING, 1985, 6 (02): : 111 - 123
[27] Bifurcations and dynamics of a discrete predator-prey system
Asheghi, Rasoul
JOURNAL OF BIOLOGICAL DYNAMICS, 2014, 8 (01) : 161 - 186
[28] Hopf Bifurcations in a Predator-Prey Model with an Omnivore
Li, Yongjun
Romanovski, Valery G.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2019, 18 (03) : 1201 - 1224
[29] Bifurcations in a predator-prey model with diffusion and memory
Aly, Shaban
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2006, 16 (06): : 1855 - 1863
[30] BIFURCATIONS AND CHAOS IN A PERIODIC PREDATOR-PREY MODEL
Kuznetsov, Yu A.
Muratori, S.
Rinaldi, S.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1992, 2 (01): : 117 - 128

← 1 2 3 4 5 →