On the number of limit cycles of a cubic near-Hamiltonian system
type: Item
instance of: scholarly article
title: On the number of limit cycles of a cubic near-Hamiltonian system
zbMATH Open document ID: 1181.34043
author: Junmin Yang
author: Maoan Han
published in: Discrete and Continuous Dynamical Systems
publication date: 2009-07-02T00:00:00Z
review text: By using a suitable first order Melnikov function the authors investigate homoclinic bifurcations for the following near-Hamiltonian cubic system \[ \dot{x}= y + \varepsilon P(x,y), \;\dot{y}= x - x^2 + \varepsilon Q(x,y), \] where \(P(x,y)\) and \(Q(x,y)\) are cubic polynomials of \(x, y\). It is proved that this system can have \(5\) limit cycles with \(3\) of them being in a neighborhood of the homoclinic loop of the unperturbed system.
reviewed by: Alexander Grin
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 37G99
Mathematics Subject Classification ID: 34C37
zbMATH DE Number: 5574113
zbMATH Keywords: near-Hamiltonian cubic system
zbMATH Keywords: Melnikov function
zbMATH Keywords: limit cycle
zbMATH Keywords: bifurcation
zbMATH Keywords: homoclinic loop
zbMATH Keywords: 16-th Hilbert's problem
MaRDI profile type: Publication
full work available at URL: dcds.2009.24.827
OpenAlex ID: W2050947024
DOI: 10.3934/DCDS.2009.24.827
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description: scientific article; zbMATH DE number 5574113