Hopf bifurcation for a \(\varphi \)-Laplacian Liénard system
type: Item
instance of: scholarly article
title: Hopf bifurcation for a \(\varphi \)-Laplacian Liénard system
zbMATH Open document ID: 1396.34021
author: Feng Liang
author: Tao Feng
published in: Qualitative Theory of Dynamical Systems
publication date: 2018-06-20T00:00:00Z
review text: Consider the planar system \[ \dot x= y\varphi'(y),\;\dot y=-g(x)- f(x,a)y\tag{\(*\)} \] near the equilibrium point at the origin, where \(a\in\mathbb{R}^m\) is a parameter vector. \((*)\) is equivalent to the \(\varphi\)-Laplacian Liénard equation \[ (\varphi(x')'+ f(x,a) x'+ g(x)= 0. \] The authors determine the cyclicity of the origin (maximum number of limit cycles bifurcating from the origin) under some conditions on \(\varphi\), \(f\) and \(g\).
reviewed by: Klaus R. Schneider
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 37G15
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 6891606
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: cyclicity
zbMATH Keywords: \(\varphi \)-Laplacian
zbMATH Keywords: Liénard system
MaRDI profile type: Publication
full work available at URL: s12346-016-0217-9
OpenAlex ID: W2554997168
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DOI: 10.1007/S12346-016-0217-9
description: scientific article; zbMATH DE number 6891606