WIAS Preprint No. 1242, (2007)

On the construction of bifurcation curves related to limit cycles of multiplicity three for planar vector fields


  • Cherkas, Leonid
  • Grin, Alexander
  • Schneider, Klaus R.

2010 Mathematics Subject Classification

  • 34C05 34C23


  • Multiple limit cycle, degenerate Hopf bifurcation, continuation method




For plane vector fields depending on three parameters we describe an algorithm to construct a curve in the parameter space such that to each point of this curve there belongs a vector field possessing a limit cycle of multiplicity three. One point of this curve is related to the bifurcation of a limit cycle of multiplicity three from an equilibrium point. The underlying procedure is a continuation method.

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