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

J. H.P. Dawes

Research output: Contribution to journal › Article

5 Citations (Scopus)

Abstract

The Hopf bifurcation with D4 ⋉ T2 symmetry generically has open regions of the normal form coefficient space where 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 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 coefficient space omitted by Silber and Knobloch [1] and completes their analysis.

Original languageEnglish
Pages (from-to)158-165
Number of pages8
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Volume262
Issue number2-3
DOIs
Publication statusPublished - 1 Nov 1999

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symmetry
planforms
coefficients

Keywords

  • Quasiperiodic solutions
  • Symmetric bifurcation theory

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Stable quasiperiodic solutions in the Hopf bifurcation with D4 ⋉ T2 symmetry. / Dawes, J. H.P.

In: Physics Letters, Section A: General, Atomic and Solid State Physics, Vol. 262, No. 2-3, 01.11.1999, p. 158-165.

Research output: Contribution to journal › Article

Dawes, JHP 1999, 'Stable quasiperiodic solutions in the Hopf bifurcation with D4 ⋉ T2 symmetry', Physics Letters, Section A: General, Atomic and Solid State Physics, vol. 262, no. 2-3, pp. 158-165. https://doi.org/10.1016/S0375-9601(99)00653-2
Dawes JHP. Stable quasiperiodic solutions in the Hopf bifurcation with D4 ⋉ T2 symmetry. Physics Letters, Section A: General, Atomic and Solid State Physics. 1999 Nov 1;262(2-3):158-165. https://doi.org/10.1016/S0375-9601(99)00653-2
Dawes, J. H.P. / Stable quasiperiodic solutions in the Hopf bifurcation with D4 ⋉ T2 symmetry. In: Physics Letters, Section A: General, Atomic and Solid State Physics. 1999 ; Vol. 262, No. 2-3. pp. 158-165.
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