WIAS Preprint No. 2422, (2017)

New approach to study the van der Pol equation for large damping



Authors

  • Schneider, Klaus

2010 Mathematics Subject Classification

  • 34C05 34C26 34D20

Keywords

  • relaxation oscillation, Dulac-Cherkas function, rotated vector field

DOI

10.20347/WIAS.PREPRINT.2422

Abstract

We present a new approach to establish the existence of a unique limit cycle for the van der Pol equation in case of large damping which is hyperbolic and stable. The proof is based on a linear time scaling (instead of the nonlinear Liénard transformation), on a Dulac--Cherkas function and the property of rotating vector fields.

Download Documents