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A perturbed Hopf bifurcation with reflection symmetry

Published online by Cambridge University Press:  14 November 2011

Wayne Nagata
Wayne Nagata
Affiliation:
Department of Mathematics, The University of British Columbia, 121-1984 Mathematics Rd, Vancouver, B. C. Canada V6T 1Y4
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Synopsis

We study the effects of a small symmetry breaking perturbation on a system of differential equations at a coupled Hopf bifurcation with O(2) symmetry, where the perturbation breaks the continuous rotation symmetry, but retains a reflection (Z2) symmetry. It is shown that for a large range of parameter values, the invariant manifolds of the unperturbed bifurcation persist and that for some values of normal form coefficients there are secondary bifurcations of nonsymmetric periodic standing wave solutions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 117 , Issue 1-2 , 1991 , pp. 1 - 20
Copyright
Copyright © Royal Society of Edinburgh 1991

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References

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