Bifurcation at Infinity in Polynomial Vector Fields

Terence R Blows, C. Rousseau

Research output: Contribution to journalArticle

57 Citations (Scopus)

Abstract

We study here the appearance of limit cycles from the equator in polynomial vector fields with no singular points at infinity: this bifurcation is a generalized Hopf bifurcation from the point at infinity. We start with the general theory and then specialize to the particular case of cubic polynomial systems for which we study the simultaneous bifurcation of limit cycles from the origin and from the equator. We finally discuss the transformation of a weak focus at infinity into a finite weak focus.

Original languageEnglish (US)
Pages (from-to)215-242
Number of pages28
JournalJournal of Differential Equations
Volume104
Issue number2
DOIs
StatePublished - Aug 1993

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Polynomial Vector Fields
Bifurcation (mathematics)
Equator
Bifurcation
Infinity
Polynomials
Limit Cycle
Hopf bifurcation
Polynomial Systems
Singular Point
Hopf Bifurcation

ASJC Scopus subject areas

  • Analysis

Cite this

Bifurcation at Infinity in Polynomial Vector Fields. / Blows, Terence R; Rousseau, C.

In: Journal of Differential Equations, Vol. 104, No. 2, 08.1993, p. 215-242.

Research output: Contribution to journalArticle

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