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 language | English |
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Pages (from-to) | 158-165 |
Number of pages | 8 |
Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |
Volume | 262 |
Issue number | 2-3 |
DOIs | |
Publication status | Published - 1 Nov 1999 |
Keywords
- Quasiperiodic solutions
- Symmetric bifurcation theory
ASJC Scopus subject areas
- Physics and Astronomy(all)