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Dynamics near a symmetric Hopf bifurcation
Published online by Cambridge University Press: 14 November 2011
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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