Stochastic stability analysis of a reduced galactic dynamo model with perturbed {\alpha}-effect

TL;DR

This paper analyzes the stability of a simplified galactic dynamo model under stochastic perturbations in the {\

Contribution

It introduces a stochastic stability analysis of a reduced galactic dynamo model, highlighting the impact of {\

Findings

Identifies regions of probabilistic stability and instability.

Shows the influence of stochastic perturbations on magnetic field quenching.

Provides visual insights into the effects of drift non-normality.

Abstract

We investigate the asymptotic behaviour of a reduced {\alpha}{\Omega}-dynamo model of magnetic field generation in spiral galaxies where fluctuation in the {\alpha}-effect results in a system with state-dependent stochastic perturbations. By computing the upper Lyapunov exponent of the linearised model, we can identify regions of instability and stability in probability for the equilibrium of the nonlinear model; in this case the equilibrium solution corresponds to a magnetic field that has undergone catastrophic quenching. These regions are compared to regions of exponential mean-square stability and regions of sub- and super-criticality in the unperturbed linearised model. Prior analysis in the literature which focuses on these latter regions does not adequately address the corresponding transition in the nonlinear stochastic model. Finally we provide a visual representation of the influence of drift non-normality and perturbation intensity on these regions.