Relaxation oscillations in a class of predator-prey systems.
type: Item
instance of: scholarly article
title: Relaxation oscillations in a class of predator-prey systems.
zbMATH Open document ID: 1094.34025
DOI: 10.1016/S0022-0396(02)00076-1
author: Weishi Liu
author: Dongmei Xiao
author: Yingfei Yi
published in: Journal of Differential Equations
publication date: 2003-04-02T00:00:00Z
review text: We consider a class of three-dimensional, singularly perturbed predator-prey systems having two predators competing exploitatively for the same prey in a constant environment. By using dynamical system techniques and the geometric singular perturbation theory, we give precise conditions which guarantee the existence of stable relaxation oscillations for systems within the class. Such result shows the coexistence of the predators and the prey with quite diversified time response which typically happens when the prey population grows much faster than those of predators. As an application, a well-known model is discussed in detail by showing the existence of stable relaxation oscillations for a wide range of parameter values of the model.
Mathematics Subject Classification ID: 34C26
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34A26
Mathematics Subject Classification ID: 34C60
zbMATH DE Number: 1891271
zbMATH Keywords: predator-prey system
zbMATH Keywords: singular perturbation
zbMATH Keywords: relaxation oscillation
zbMATH Keywords: stability
MaRDI profile type: Publication
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full work available at URL: s0022-0396(02)00076-1
OpenAlex ID: W2030813019
description: scientific article; zbMATH DE number 1891271