Bifurcation of limit cycles at infinity in piecewise polynomial systems
type: Item
instance of: scholarly article
title: Bifurcation of limit cycles at infinity in piecewise polynomial systems
zbMATH Open document ID: 1387.34059
author: Ting Chen
author: P. Yu
author: Lihong Huang
author: Wentao Huang
published in: Nonlinear Analysis. Real World Applications
publication date: 2018-02-15T00:00:00Z
review text: This paper is a contribution to the theory of bifurcations of limit cycles of planar polynomial vector fields. The first result is a recursive algorithm for the computation of the Lyapunov constants at infinity in piecewise polynomial systems with no singular points at infinity. Furthermore, this method is used to study limit cycle bifurcations in cubic polynomial systems. In particular, conditions for simultaneous Hopf bifurcations at the origin and at infinity are established. As an example, the results are applied to a concrete system to show the existence of exactly 11 limit cycles bifurcating from infinity.
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34A36
zbMATH DE Number: 6839537
zbMATH Keywords: polynomial vector field
zbMATH Keywords: bifurcation
zbMATH Keywords: limit cycle
reviewed by: Vladimir Jacimovic
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2017.10.003
OpenAlex ID: W2767997111
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DOI: 10.1016/J.NONRWA.2017.10.003
description: scientific article; zbMATH DE number 6839537