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Dynamics near a symmetric Hopf bifurcation

Published online by Cambridge University Press:  14 November 2011

Wayne Nagata
Wayne Nagata
Affiliation:
Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada, NIG 2W1
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Synopsis

We consider the effects of a small symmetry breaking perturbation on a system of differential equations near a Hopf bifurcation point, where the unperturbed system has O(2) symmetry. We show that there exist secondary bifurcations of invariant two-tori of solutions and that the flow on the tori can be quasiperiodic or weakly resonant (phase locked), depending on the size of the perturbation.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 108 , Issue 3-4 , 1988 , pp. 249 - 267
Copyright
Copyright © Royal Society of Edinburgh 1988

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