Delayed stability switches in singularly perturbed predator-prey models

被引：3
|
作者：
Banasiak, J. [1 ,2 ]
Tchamga, M. S. Seuneu [3 ]
机构：
[1] Univ Pretoria, Dept Math & Appl Math, Pretoria, South Africa
[2] Tech Univ Lodz, Inst Math, Lodz, Poland
[3] Univ KwaZulu Natal, Sch Math Sci, ZA-4041 Durban, South Africa
来源：
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2017年 / 35卷
关键词：
Singularly perturbed dynamical systems; Multiple time scales; Tikhonov theorem; Delayed stability switch; Predator-prey models; Canard solutions; AUTONOMOUS SYSTEMS; LIMIT-CYCLES; BIFURCATION; MANIFOLDS; EXCHANGE;
D O I：
10.1016/j.nonrwa.2016.10.013
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we provide an elementary proof of the existence of canard solutions for a class of singularly perturbed planar systems in which there occurs a transcritical bifurcation of the quasi steady states. The proof uses the one-dimensional result proved by V.F. Butuzov, N.N. Nefedov and K.R. Schneider, and an appropriate monotonicity assumption on the vector field. The result is applied to identify all possible predator prey models with quadratic vector fields allowing for the existence of canard solutions. (C) 2016 Elsevier Ltd. All rights reserved.
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页码：312 / 335
页数：24
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