Limit cycles for two families of cubic systems
type: Item
instance of: scholarly article
title: Limit cycles for two families of cubic systems
zbMATH Open document ID: 1259.34022
author: Armengol Gasull
author: M. J. Álvarez
author: Rafel Prohens
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2012-10-11T00:00:00Z
full work available at URL: http://ddd.uab.cat/record/150519
review text: The authors study the number of limit cycles of two families of cubic systems representing models of real phenomena. The first one has the form \[ \dot{x}=A(1-x-y)-B xy^2, \;\;\dot{y}=-y(1-x-y)+Bxy^2, \] where \(A\) and \(B\) are positive real parameters. It is motivated by a model of star formation histories in giant spiral galaxies. The second one comes from a model of Volterra type and has the form \[ \dot{x}=x(x(1-x)-(x+n)y), \;\;\dot{y}=y(x+n)(x-m), \] where \(m\) and \(n\) are positive real parameters. To prove the main results on the existence of periodic orbits, the authors extend a criterion on the uniqueness of limit cycles due to Kuang and Freedman and construct of a suitable Dulac function.
reviewed by: Alexander Grin
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34C60
zbMATH DE Number: 6092713
zbMATH Keywords: cubic system
zbMATH Keywords: Kolmogorov system
zbMATH Keywords: limit cycle
zbMATH Keywords: bifurcation
MaRDI profile type: Publication
OpenAlex ID: W2044872422
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DOI: 10.1016/J.NA.2012.07.012
description: scientific article; zbMATH DE number 6092713