### Abstract

Structurally stable heteroclinic cycles (SSHCs) are proposed as the mathematical structures that are responsible for the reversals of dipolar magnetic fields in spherical dynamos. The existence of SSHCs involving dipolar magnetic fields generated by convection in a spherical shell for a non-rotating sphere is rigorously proven. The possibility of SSHCs in a rotating shell is proposed, and their existence in a low-dimensional model of the magnetohydrodynamic equations is numerically confirmed. The resulting magnetic time-series shows a dipolar magnetic field, aligned with the rotation axis that intermittently becomes unstable, changes the polar axis, starts rotating, disappears completely and eventually re-establishes itself in its original or opposite direction, chosen randomly.

Original language | English (US) |
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Pages (from-to) | 577-596 |

Number of pages | 20 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 459 |

Issue number | 2031 |

DOIs | |

State | Published - Mar 8 2003 |

### Keywords

- Heteroclinic cycles
- Reversals
- Spherical dynamos

### ASJC Scopus subject areas

- Mathematics(all)
- Engineering(all)
- Physics and Astronomy(all)