  We consider a neuronal levels model that exhibits critical avalanches
satisfying power-law distribution. The model has recently explained a change in
the scaling exponent from 3/2 to 5/4, accounting for a change in the drive
condition from no input to moderate strength, along with a relaxed separation
of time-scale between drive and dissipation. To understand the robustness of
the scaling features, we examine the effect of different noisy stimuli in the
moderate input regime. Our tool of analysis is the scaling method. We compute
scaling functions associated with the avalanche size distribution, revealing
striking finite-size scaling. For a class of noisy drives, we find that the
scaling exponent can take a value different from 5/4, with an explicit system
size dependence of the distribution.
