On the lack of analytic solutions of the Van der Pol oscillator

D. E. Panayotounakos, N. D. Panayotounakou, A. F. Vakakis

Research output: Contribution to journalArticle

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 e 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).

Original languageEnglish (US)
Pages (from-to)611-615
Number of pages5
JournalZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
Volume83
Issue number9
DOIs
StatePublished - Dec 1 2003

Keywords

  • Asymptotic solutions
  • Van der Pol oscillator

ASJC Scopus subject areas

  • Computational Mechanics
  • Applied Mathematics

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