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.