Cyclicity of some Liénard systems
type: Item
instance of: scholarly article
title: Cyclicity of some Liénard systems
zbMATH Open document ID: 1332.34068
author: Na Li
author: Valery G. Romanovski
author: Maoan Han
published in: Communications on Pure and Applied Analysis
publication date: 2015-10-16T00:00:00Z
review text: The paper is devoted to the cyclicity problem of two families of Liénard systems \[ \dot{x}=y-\frac{q_n(x)}{(1-x)^m}, \quad \dot{y}=-g(x) \] and \[ \dot{x}=y-\frac{q_n(x)}{(1-\alpha x)(1-\beta x)}, \quad \dot{y}=-g(x), \quad \alpha\beta\neq 0, \] where \(q_n(x)=\sum_{i=0}^n a_ix^i\) and \(g(x)\) satisfies the following conditions \[ g(0)=0, \quad g'(0)>0, \quad g(-x)=-g(x). \] The authors study small-amplitude limit cycles and find the exact number of such limit cycles bifurcating from a center or focus at the origin for these families.
reviewed by: Alexander Grin
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 37G15
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 6495273
zbMATH Keywords: limit cycle
zbMATH Keywords: cyclicity
zbMATH Keywords: Liénard system
MaRDI profile type: Publication
full work available at URL: cpaa.2015.14.2127
OpenAlex ID: W2524714693
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DOI: 10.3934/CPAA.2015.14.2127
description: scientific article; zbMATH DE number 6495273