  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.
