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
Issue number2-3
Publication statusPublished - 1 Nov 1999


  • Quasiperiodic solutions
  • Symmetric bifurcation theory

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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