Bifurcations of limit cycles in a reversible quadratic system with a center, a saddle and two nodes
type: Item
instance of: scholarly article
title: Bifurcations of limit cycles in a reversible quadratic system with a center, a saddle and two nodes
zbMATH Open document ID: 1198.34049
author: Chengzhi Li
author: Jiang Yu
author: Iliya D. Iliev
published in: Communications on Pure and Applied Analysis
publication date: 2010-05-27T00:00:00Z
review text: Consider the system \[ \dot{x}=-y-3x^{2}+by^{2},\quad\dot{y}=x(1-2y), \] where \(b\) is a real parameter. The exact upper bound for the number of limit cycles produced by the period annulus of the system under quadratic perturbations is called the cyclicity of the period annulus. By using the properties of related complete elliptic integrals and the geometry of some plane curves, the authors prove that, if \(b \geq 2\), \(b\neq 3\), then the cyclicity of the period annulus is two. This bound is exact.
reviewed by: M. A. M. Alwash
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C08
Mathematics Subject Classification ID: 37G15
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C14
zbMATH DE Number: 5713045
zbMATH Keywords: bifurcation
zbMATH Keywords: period annulus
zbMATH Keywords: complete elliptic integrals
zbMATH Keywords: limit cycles
MaRDI profile type: Publication
full work available at URL: cpaa.2010.9.583
OpenAlex ID: W2081892360
DOI: 10.3934/CPAA.2010.9.583
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description: scientific article; zbMATH DE number 5713045