Homoclinic bifurcation in a predator-prey model
type: Item
instance of: scholarly article
title: Homoclinic bifurcation in a predator-prey model
zbMATH Open document ID: 0915.34028
DOI: 10.1023/A:1006508529250
author: L. Niño
author: Marcos Lizana
published in: Acta Mathematica Hungarica
publication date: 1999-03-14T00:00:00Z
review text: The authors deal with predator-prey models \[ N' = N \Biggl[ \frac{\varepsilon}{K}(K - N) - \frac{aP}{\beta + N}\Biggr], \quad P' = P \Biggl[-M(P) + \frac{bN}{\beta + N}\Biggr], \tag{1} \] where \(N(t)\) and \(P(t)\) are the quantities of prey and predator, respectively, the function \(M(P) = (\gamma + \delta P) / (1 + P)\) describes the specific mortality of predators in absence of prey. They consider codimension-2 bifurcations which occur in some two-dimensional parameter region. There is a continuous curve in the parameter region for which system (1) has a homoclinic orbit. The homoclinic orbit bifurcates generating a locally unique periodic orbit.
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34C37
zbMATH DE Number: 1261149
zbMATH Keywords: predator-prey model
zbMATH Keywords: homoclinic bifurcation
reviewed by: Victor I. Tkachenko
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1261149