Multiple limit cycle bifurcation surfaces and global families of multiple limit cycles
type: Item
instance of: scholarly article
title: Multiple limit cycle bifurcation surfaces and global families of multiple limit cycles
zbMATH Open document ID: 0837.34046
published in: Journal of Differential Equations
publication date: 1996-05-13T00:00:00Z
review text: ``Sufficient conditions are given for the local existence of multiplicity-\(m\) limit cycle bifurcation surfaces, \(C_m\), of planar analytic systems depending on \(n\) parameters with \(n \geq m \geq 2\). In the generic case, the surfaces \(C_2\), \(C_3\), and \(C_4\) are the familiar saddle-node, cusp, and swallow-tail bifurcation surfaces, respectively. The author's termination principle for global one-parameter families of simple limit cycles of relatively prime, planar, analytic systems is generalized to a termination principle for global one- parameter families of multiple limit cycles which implies that the boundary of a global limit cycle bifurcation surface typically consists of Hopf bifurcation surfaces and/or homoclinic (or heteroclinic) loop bifurcation surfaces''.
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 37G15
zbMATH DE Number: 810064
zbMATH Keywords: limit cycle bifurcation surfaces
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: loop bifurcation
author: Lawrence M. Perko
reviewed by: C. Chicone
MaRDI profile type: Publication
full work available at URL: jdeq.1995.1140
OpenAlex ID: W2094893378
DOI: 10.1006/JDEQ.1995.1140
description: scientific article; zbMATH DE number 810064