Relaxation oscillations and canard explosion in a predator-prey system of Holling and Leslie types

被引：24

作者：

Atabaigi, Ali ^{[1
]}

Barati, Ali ^{[2
]}

机构：

[1] Razi Univ, Dept Math, Kermanshah 6714967346, Iran

[2] Razi Univ, Eslam Abad Gharb Fac Engn, Kermanshah, Iran

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2017年 / 36卷

关键词：

Relaxation oscillations; Canard explosion; Geometric singular perturbation theory; Predator-prey system; Holling and Leslie; SINGULAR PERTURBATION-THEORY; LIMIT-CYCLES; BIFURCATIONS;

D O I：

10.1016/j.nonrwa.2017.01.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give a geometric analysis of relaxation oscillations and canard cycles in a singularly perturbed predator prey system of Honing and Leslie types. We discuss how the canard cycles are found near the Hopf bifurcation points. The transition from small Hopf-type cycles to large relaxation cycles is also discussed. Moreover, we outline one possibility for the global dynamics. Numerical simulations are also carried out to verify the theoretical results. (C) 2017 Elsevier Ltd. All rights reserved.

引用

页码：139 / 153

页数：15

共 18 条

[1]

Bazykin AD, 1998, NONLINEAR DYNAMICS I, V11

[2] The entry-exit function and geometric singular perturbation theory [J].