Global bifurcation analysis of a class of planar systems
- Grin, Alexander
- Schneider, Klaus R.
2010 Mathematics Subject Classification
- 34C05 34C23 34D20
- Global bifurcation limit cycle, planar autonomous system, Dulac--Cherkas function, rotated vector field, singularly perturbed system
We consider planar autonomous systems dx/dt =P(x,y,λ), dy/dt =Q(x,y,λ) depending on a scalar parameter λ. We present conditions on the functions P and Q which imply that there is a parameter value λ0 such that for &lambda > λ0 this system has a unique limit cycle which is hyperbolic and stable. Dulac-Cherkas functions, rotated vector fields and singularly perturbed systems play an important role in the proof.