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

Panayotounakos, DE; Panayotounakou, ND; Vakakis, AF

dc.contributor.author	Panayotounakos, DE	en
dc.contributor.author	Panayotounakou, ND	en
dc.contributor.author	Vakakis, AF	en
dc.date.accessioned	2014-03-01T01:19:21Z
dc.date.available	2014-03-01T01:19:21Z
dc.date.issued	2003	en
dc.identifier.issn	0044-2267	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/15448
dc.subject	Asymptotic solutions	en
dc.subject	Van der Pol oscillator	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Mechanics	en
dc.subject.other	COUPLED VANDERPOL OSCILLATORS	en
dc.title	On the lack of analytic solutions of the Van der Pol oscillator	en
heal.type	journalArticle	en
heal.identifier.primary	10.1002/zamm.200310040	en
heal.identifier.secondary	http://dx.doi.org/10.1002/zamm.200310040	en
heal.language	English	en
heal.publicationDate	2003	en
heal.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(epsilon(-2)). (C) 2003 WILEY-VCH Vertag GmbH & Co. KGaA, Weinheim.	en
heal.publisher	WILEY-V C H VERLAG GMBH	en
heal.journalName	ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik	en
dc.identifier.doi	10.1002/zamm.200310040	en
dc.identifier.isi	ISI:000185308700005	en
dc.identifier.volume	83	en
dc.identifier.issue	9	en
dc.identifier.spage	611	en
dc.identifier.epage	615	en