Limit cycles of a \(Z_3\)-equivariant near-Hamiltonian system
type: Item
instance of: scholarly article
title: Limit cycles of a \(Z_3\)-equivariant near-Hamiltonian system
zbMATH Open document ID: 1180.34031
author: Hongyan Ma
author: Maoan Han
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2009-07-10T00:00:00Z
review text: The authors study the number of limit cycles number for the following near-Hamiltonian polynomial system \[ \dot x= 3y+ 8xy+ x^2y+y^3+ \varepsilon p(x,y), \quad \dot y= -3x+ 4x^2- 4y^2- x^3- xy^2+ \varepsilon q(x,y), \] where \(\varepsilon \geq 0\) is a small real parameter, \(p\) and \(q\) are polynomials of degree 5, 4 or 3. By using the method of Melnikov function it is proved that such a system with degrees 3, 4 and 5 can has 4, 10 and 15 limit cycles, respectively. The corresponding distributions of limit cycles are given.
reviewed by: Alexander Grin
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 5577452
zbMATH Keywords: near-Hamiltonian system
zbMATH Keywords: limit cycle
zbMATH Keywords: bifurcation
zbMATH Keywords: Melnikov function
zbMATH Keywords: \(Z_3\)-equivariance
MaRDI profile type: Publication
full work available at URL: j.na.2009.02.054
OpenAlex ID: W1968300058
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DOI: 10.1016/J.NA.2009.02.054
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description: scientific article; zbMATH DE number 5577452