The center conditions and local bifurcation of critical periods for a Liénard system
type: Item
instance of: scholarly article
title: The center conditions and local bifurcation of critical periods for a Liénard system
zbMATH Open document ID: 1218.34034
author: Qiujin Xu
author: Wentao Huang
published in: Applied Mathematics and Computation
publication date: 2011-03-28T00:00:00Z
review text: The authors study the two dimensional system \[ \dot x = y,\quad \dot y = -g(x) - f(x) y \] of differential equations that is equivalent to the Liénard system \(\ddot x + f(x) \dot x + g(x) = 0\) in the special case that \(f(x) = a_1 x + a_2 x^2 + a_3 x^3 + a_4 x^4\) and \(g(x) = x + b_2 x^2 + b_3 x^3 + b_4 x^4\). They characterize the existence of a center at the origin, its degeneracy, and isochronicity, and count the number of critical periods that can bifurcate from the origin.
reviewed by: Douglas S. Shafer
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 5870930
zbMATH Keywords: Lienard system
zbMATH Keywords: center problem
zbMATH Keywords: isochronous centers
zbMATH Keywords: critical periods
MaRDI profile type: Publication
full work available at URL: j.amc.2011.01.035
OpenAlex ID: W1974879860
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DOI: 10.1016/J.AMC.2011.01.035
description: scientific article; zbMATH DE number 5870930