Chaotic transients and hysteresis in an α ² dynamo model

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.

Subcritical dynamo and hysteresis in a Babcock-Leighton type kinematic dynamo model

“…Later dynamo hysteresis was confirmed in magnetohydrodynamics (MHD) simulations of the helical turbulent dynamo with imposed shear (Karak et al 2015). Recently this was also seen in numerical simulations of turbulent α 2 dynamo (Oliveira et al 2021).…”

Focusing on transient chaos

“…In this section, we provide an overview of contributions to the focus issue, which describe the emergence of transient chaos in various applications, including self-organization of active particles [8], dynamics of power grids [9], applications in medicine [10] and magnetohydrodynamics [11], as well as in machine learning [12].…”

“…The paper by Oliveira et al [11] investigates a dynamo model with the helicity as a control parameter. The transition to dynamo occurs via a hysteretic blowout bifurcation associated with a sudden increase in the magnetic energy.…”