On the lack of analytic solutions of the Van der Pol oscillator
D.E. Panayotounakos, N.D. Panayotounakou, A.F. Vakakis
Source record
Source: Crossref
Published: Aug 5, 2003
DOI: 10.1002/zamm.200310040
Open original source ↗Source abstract
Abstract In this work it is shown that by a series of transformations the classical Van der Pol oscillator can be exactly reduced to Abel's equations of the second kind. The absence of exact analytic solutions in terms of known (tabulated) functions of the reduced equations leads to the conclusion that there are no exact solutions of the Van der Pol oscillator in terms of known (tabulated) functions. In the limits or small or large values of the parameter ϵ the reduced equations are amenable to asymptotic analysis. For the case of large values of the parameter (relaxation oscillations) an analytic solution to the problem is provided that is exact up to O (ϵ ‐2 ).
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.