Chaotic transients and hysteresis in an $\alpha^{2}$ dynamo model

TL;DR

This paper investigates chaotic transients and hysteresis in a nonlinear $
^{2}$ dynamo model through numerical simulations, revealing bifurcations and crises that cause sudden changes in magnetic energy.

Contribution

It introduces the role of hysteretic blowout bifurcations and boundary crises in the transition to dynamo states within an $
^{2}$ model.

Findings

Identification of hysteretic blowout bifurcation leading to dynamo transition.

Discovery of boundary crisis destroying high-energy attractor.

Observation of long chaotic transients due to chaotic saddle and relative attractor.

Abstract

The presence of chaotic transients in a nonlinear dynamo is investigated through numerical simulations of the 3D magnetohydrodynamic equations. By using the kinetic helicity of the flow as a control parameter, a hysteretic blowout bifurcation is conjectured to be responsible for the transition to dynamo, leading to a sudden increase in the magnetic energy of the attractor. This high-energy hydromagnetic attractor is suddenly destroyed in a boundary crisis when the helicity is decreased. Both the blowout bifurcation and the boundary crisis generate long chaotic transients that are due, respectively, to a chaotic saddle and a relative chaotic attractor.