Abstract
Structurally stable heteroclinic cycles (SSHCs) are proposed as the mathematical structures that are responsible for the reversals of dipolar magnetic › elds in spherical dynamos. The existence of SSHCs involving dipolar magnetic › elds 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 lowdimensional model of the magnetohydrodynamic equations is numerically con› rmed. The resulting magnetic time-series shows a dipolar magnetic › eld, 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.
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Schedule a callMore From: Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
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