Phase portraits of the Higgins-Selkov system
type: Item
instance of: scholarly article
title: Phase portraits of the Higgins-Selkov system
zbMATH Open document ID: 1492.34056
author: Jaume Llibre
author: Marzieh Mousavi
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2022-01-06T00:00:00Z
review text: Consider the planar autonomous system \[ \frac{dx}{dt}= (1-x^\gamma), \quad \frac{dy}{dt} =\alpha y(xy^{\gamma - 1} -1), \tag{1} \] where \(\alpha\) is a real number and \(\gamma > 1\) an integer. In case \(\gamma = 2\), system (1) has been used by E.E. Selkov to model glycolysis, the corresponding phase portrait has been investigated completely by \textit{J. C. Artés} et al. [Chaos Solitons Fractals 114, 145--150 (2018; Zbl 1415.34058)] and \textit{R. Mohanasubha} et al. [Springer Proc. Math. Stat. 266, 75--103 (2018; Zbl 1419.34116)]. The authors of the paper under review determine the phase portraits of (1) for \( \gamma = 3,4,5,6 \) in the Poincaré disc. Especially they prove that if system (1) has a limit cycle then this cycle is unique.
Mathematics Subject Classification ID: 34C60
Mathematics Subject Classification ID: 92C45
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C07
zbMATH DE Number: 7452629
zbMATH Keywords: Higgins-Selkov system
zbMATH Keywords: limit cycle
zbMATH Keywords: phase portrait
zbMATH Keywords: Poincaré compactification
reviewed by: Klaus R. Schneider
MaRDI profile type: Publication
full work available at URL: dcdsb.2021039
OpenAlex ID: W3125762763
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DOI: 10.3934/DCDSB.2021039
description: scientific article; zbMATH DE number 7452629