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 . 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  and completes their analysis.
|Number of pages||8|
|Journal||Physics Letters, Section A: General, Atomic and Solid State Physics|
|Publication status||Published - 1 Nov 1999|
- Quasiperiodic solutions
- Symmetric bifurcation theory
ASJC Scopus subject areas
- Physics and Astronomy(all)