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Stable quasiperiodic solutions in the Hopf bifurcation with D4⋉T2 symmetry

✍ Scribed by J.H.P. Dawes

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
223 KB
Volume
262
Category
Article
ISSN
0375-9601

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✦ Synopsis

The Hopf bifurcation with D h T 2 symmetry generically has open regions of the normal form coefficient space where 4 w x all branches of periodic solutions bifurcate supercritically but none is stable 1 . In such regions we prove the existence of an attracting set near the origin. A new possibility for the attractor is a quasiperiodic solution branch related to Standing Cross Ž . Rolls SCR . The new solution physically represents a planform we call Drifting Standing Cross Rolls. Unlike Standing Cross Rolls, this solution can be stable, as can a further triply-periodic solution. This explains the behaviour in the regions of w x coefficient space omitted by Silber and Knobloch 1 and completes their analysis.

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