Organizing center for the bifurcation analysis of a generalized Gause model with prey harvesting and Holling response function of type III
type: Item
instance of: scholarly article
title: Organizing center for the bifurcation analysis of a generalized Gause model with prey harvesting and Holling response function of type III
zbMATH Open document ID: 1236.34059
author: Sophie Laurin
author: Christiane Rousseau
published in: Journal of Differential Equations
publication date: 2011-10-12T00:00:00Z
review text: This note is an addendum to the paper [\textit{R. M. Etoua} and \textit{C. Rousseau}, J. Differ. Equations 249, No. 9, 2316--2356 (2010; Zbl 1217.34080)], where a generalized Gause model with prey harvesting and a generalized Holling response function of type III: \(p(x)={m x^2 \over a x^2 + b x + 1}\) was studied and complete bifurcation diagrams were proposed. A conjecture was proposed for a nilpotent point of saddle type lying on an invariant line and of codimension greater than or equal to 3. It was conjectured that the nilpotent point is of infinite codimension for \(b=0\). This conjecture was in line with a second conjecture about the codimension of Hopf bifurcation for \(b=0\). These two conjectures are proved in this note. The method of proof is quite original. It consists in finding analytic transformation and time scaling of the system bringing it to a time-reversible system.
reviewed by: Jinzhi Lei
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C60
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 5957032
zbMATH Keywords: generalized Gause model with prey harvesting
zbMATH Keywords: Holling response function of type III
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: nilpotent saddle bifurcation
MaRDI profile type: Publication
full work available at URL: j.jde.2011.04.017
OpenAlex ID: W2021377296
cites work: Bifurcation analysis of a generalized Gause model with prey harvesting and a generalized Holling response function of type III
cites work: Finite cyclicity of graphics with a nilpotent singularity of saddle or elliptic type
DOI: 10.1016/J.JDE.2011.04.017
description: scientific article; zbMATH DE number 5957032