Dynamos as dynamical systems

Phase space trajectory of a flux transport dynamo model reduced by spatial truncation to a three-dimensional dynamical system for the poloidal field amplitude (Ap), toroidal field amplitude (Bphi), and meridional flow speed (vp). The solution normally follows the limit-cycle trajectory traced by the black dashed line. In the presence of stochastic forcing, this trajectory blurs into the diffuse ring of gray points. At times, a stochastic kick forces the solution away from the attractor, leading to a collapse towards the nul magnetic field axis (dark red to light red portion of the plotted trajectory). Eventually, the solution spirals out back towards the attractor (orange to yellow portion of the trajectory), with cyclic behavior resuming. This dynamical behavior offers a possible explanatory framework for the intermittent drops in activity observed in the susnpot record.


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