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On the Detection of Limit Cycles by the Variational Velocity Method

On the Detection of Limit Cycles by the Variational Velocity Method This paper summarizes, clarifies, and corrects some aspects of the variational velocity methodfor the detection of limit cycles. After definitions and statements of the most important theoremsassociated with this method, some aspects of the proof of the main theorem are corrected andreworked. An example from the original paper in Acta Appl. Math. 48 (1997),13–32, is then discussed and criticized. Finally, the limitations of this method are discussed,especially as it applies to systems involving multiple limit cycles (and therefore as it applies toHilbert’s XVIth Problem). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

On the Detection of Limit Cycles by the Variational Velocity Method

Esch, Jesse; Rogers, Thomas
Acta Applicandae Mathematicae , Volume 54 (3) – Sep 18, 2004
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References (15)

Publisher
Springer Journals
Copyright
Copyright © 1998 by Kluwer Academic Publishers
Subject
Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Classical Mechanics
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1023/A:1006158306350
Publisher site
See Article on Publisher Site

Abstract

This paper summarizes, clarifies, and corrects some aspects of the variational velocity methodfor the detection of limit cycles. After definitions and statements of the most important theoremsassociated with this method, some aspects of the proof of the main theorem are corrected andreworked. An example from the original paper in Acta Appl. Math. 48 (1997),13–32, is then discussed and criticized. Finally, the limitations of this method are discussed,especially as it applies to systems involving multiple limit cycles (and therefore as it applies toHilbert’s XVIth Problem).

Journal

Acta Applicandae Mathematicae – Springer Journals

Published: Sep 18, 2004

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