Period-doubling/symmetry-breaking mode interactions in iterated maps

We consider iterated maps with a reflectional symmetry. Possible bifurcations in such systems include period-doubling bifurcations (within the symmetric subspace) and symmetry-breaking bifurcations. By using a second parameter, these bifurcations can be made to coincide at a mode interaction. By ref...

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Bibliographic Details
Published in:Physica. D 2009-10, Vol.238 (19), p.1992-2002
Main Authors: Aston, P.J., Mir, H.
Format: Article
Language:English
Subjects:
Coupled maps
Exact sciences and technology
Mode interaction
Period-doubling bifurcation
Physics
Symmetry-breaking bifurcation
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Summary:We consider iterated maps with a reflectional symmetry. Possible bifurcations in such systems include period-doubling bifurcations (within the symmetric subspace) and symmetry-breaking bifurcations. By using a second parameter, these bifurcations can be made to coincide at a mode interaction. By reformulating the period-doubling bifurcation as a symmetry-breaking bifurcation, two bifurcation equations with Z 2 × Z 2 symmetry are derived. A local analysis of solutions is then considered, including the derivation of conditions for a tertiary Hopf bifurcation. Applications to symmetrically coupled maps and to two coupled, vertically forced pendulums are described.
ISSN:0167-2789
1872-8022
DOI:10.1016/j.physd.2009.07.017