The convexity of closed orbits of Liénard systems
type: Item
instance of: scholarly article
title: The convexity of closed orbits of Liénard systems
zbMATH Open document ID: 1270.34048
published in: Bulletin des Sciences Mathématiques
publication date: 2013-03-15T00:00:00Z
review text: Consider the planar system \[ {dx\over dt}= F(x)- y,\quad\frac{dy}{dt}= x\tag{\(*\)} \] under the condition that \(F\in C^2(\mathbb R,\mathbb R)\) and satisfies \[ F(0)= 0\text{ and } F''(x)\neq 0\text{ for }x\in G:= \{x\in\mathbb{R}\setminus\{0\}: |F'(x)|\geq 2\}. \] In this situation, the authors prove that any closed orbit of \((*)\) is strictly convex.
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 6145432
zbMATH Keywords: closed orbit
zbMATH Keywords: convexity
zbMATH Keywords: limit cycle
zbMATH Keywords: Liénard system
zbMATH Keywords: van der Pol equation
author: Li-Jun Yang
author: Xian-Wu Zeng
reviewed by: Klaus R. Schneider
MaRDI profile type: Publication
full work available at URL: j.bulsci.2012.10.002
OpenAlex ID: W2079295795
DOI: 10.1016/J.BULSCI.2012.10.002
description: scientific article; zbMATH DE number 6145432