Stability loss delay in harvesting competing populations
type: Item
instance of: scholarly article
title: Stability loss delay in harvesting competing populations
zbMATH Open document ID: 1017.34058
author: H. Boudjellaba
author: Tewfik Sari
published in: Journal of Differential Equations
publication date: 2003-08-18T00:00:00Z
review text: Consider the differential system \[ dx/dt = xM(x,y,E), \;dy/dt=y N(x,y), \;dE/dt = \varepsilon E P(x),\tag{*} \] describing the dynamics of two competing populations \(x\) and \(y\) under a harvesting effort \(E\) with a slow growth rate \((\varepsilon\) is small). \(M\) and \(N\) are such that, in case of no harvesting, one of the species disappears. The author proves that the harvesting effort leads to the existence of a relaxation oscillation (no extinction). It is shown that the oscillation is of canard type (the phenomenon of delayed loss of stability occurs).
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 1283669
zbMATH Keywords: singular perturbation
zbMATH Keywords: competing species
zbMATH Keywords: dynamic bifurcations
zbMATH Keywords: delayed loss of stability
zbMATH Keywords: cycles
zbMATH Keywords: canard type
reviewed by: Klaus R. Schneider
MaRDI profile type: Publication
full work available at URL: jdeq.1998.3533
OpenAlex ID: W2039102999
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DOI: 10.1006/JDEQ.1998.3533
description: scientific article; zbMATH DE number 1283669