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Forcing, damping and detuning for single and coupled Van der Pol oscillators

Published online by Cambridge University Press:  20 March 2014

D. R. J. Chillingworth  and
Z. Afshar-nejad
D. R. J. Chillingworth
Affiliation:
Mathematical Studies, University of Southampton, University Road, Southampton SO17 1BJ, UK, ([email protected])
Z. Afshar-nejad
Affiliation:
Applied Mathematics Department, Ferdowsi University of Mashhad, Azadi Square, Mashad, Iran, ([email protected])
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Abstract

We use Melnikov function techniques together with geometric methods of bifurcation theory to study the interactions of forcing, damping and detuning on resonant periodic orbits for single and coupled forced Van der Pol oscillators. For a coupled pair the local bifurcation geometry is almost everywhere described in terms of the singularities of a line congruence in three dimensions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 144 , Issue 2 , April 2014 , pp. 267 - 297
Copyright
Copyright © Royal Society of Edinburgh 2014 

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