Small amplitude limit cycles of symmetric cubic systems

Terence R. Blows

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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
Issue number9
StatePublished - Nov 2008


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

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics


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