New approach to study the van der Pol equation for large damping
- Schneider, Klaus
2010 Mathematics Subject Classification
- 34C05 34C26 34D20
- relaxation oscillation, Dulac-Cherkas function, rotated vector field
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.
- Electron. J. Qual. Theory Differ. Equ., 8 (2018), pp. 1--10, DOI 10.14232/ejqtde/2018.1.8 .