Five limit cycles for a simple cubic system
type: Item
instance of: scholarly article
title: Five limit cycles for a simple cubic system
zbMATH Open document ID: 0885.34029
DOI: 10.5565/PUBLMAT_41197_12
published in: Publicacions Matemàtiques
publication date: 1998-03-30T00:00:00Z
full work available at URL: https://eudml.org/doc/41280
review text: The authors consider a system \[ x'=\lambda x+y+Ax^2+Bxy, y'=-x+\lambda y+Kx^2+Lxy+My^2+Nx^3. \] They reduce it to a Liénard-type system to find new necessary conditions for the origin to be a center. It is shown that the origin is a fine focus of maximal order five, and the corresponding Lyapunov quantities are explicitly found. It follows that a system of the considered type can have five limit cycles.
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 1057642
zbMATH Keywords: Liénard-type system
zbMATH Keywords: fine focus
zbMATH Keywords: Lyapunov quantities
zbMATH Keywords: five limit cycles
author: Noel G. Lloyd
author: Jane M. Pearson
reviewed by: Sergei Yu. Pilyugin
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1057642