WIAS Preprint No. 2426, (2017)

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.

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