Small amplitude limit cycles of symmetric cubic systems

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Hilbert's Sixteenth Problem concerns the number and relative position of limit cycles in a planar polynomial system of differential equations. We show, using multiple Hopf bifurcation from multiple fine foci, that limit cycle configurations of types (3, 3, -2, -2) and (2, 2, 1, 1, -1) occur in symmetric cubic systems.

Original languageEnglish (US)
Pages (from-to)2323-2328
Number of pages6
JournalComputers and Mathematics with Applications
Volume56
Issue number9
DOIs
StatePublished - Nov 2008

Fingerprint

Hopf bifurcation
Limit Cycle
Differential equations
Polynomials
Polynomial Systems
System of Differential Equations
Hopf Bifurcation
Hilbert
Configuration

Keywords

  • Cubic systems
  • Hilbert's Sixteenth Problem
  • Hopf bifurcation
  • Limit cycles

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Modeling and Simulation

Cite this

Small amplitude limit cycles of symmetric cubic systems. / Blows, Terence R.

In: Computers and Mathematics with Applications, Vol. 56, No. 9, 11.2008, p. 2323-2328.

Research output: Contribution to journalArticle

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