Using a one-dimensional \alpha \omega -dynamo model appropriate to galaxies , we study the possibility of dynamo action driven by a stochastic alpha effect and shear .
To determine the field evolution , one needs to examine a large number of different realizations of the stochastic component of \alpha .
The net growth or decay of the field depends not only on the dynamo parameters but also on the particular realization , the correlation time of the stochastic \alpha compared to turbulent diffusion timescale and the time over which the system is evolved .
For dynamos where both a coherent and fluctuating \alpha are present , the stochasticity of \alpha can help alleviate catastrophic dynamo quenching , even in the absence of helicity fluxes .
One can obtain final field strengths up to a fraction \sim 0.01 of the equipartition field B _ { eq } for dynamo numbers |D| \sim 40 , while fields comparable to B _ { eq } require much larger degree of \alpha fluctuations or shear .
This type of dynamo may be particularly useful for amplifying fields in the central regions of disk galaxies .