### Abstract

The Hopf bifurcation with D_{4} ⋉ T^{2} 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 |
---|---|

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)