  The statistical analysis of the collective neural activity known as
avalanches provides insight into the proper behavior of brains across many
species. We consider a neural network model based on the work of Lombardi,
Herrmann, De Arcangelis et al. that captures the relevant dynamics of neural
avalanches, and we show how tuning the fraction of inhibitory neurons in this
model alters the connectivity of the network over time, removes exponential
cut-offs present in the distributions of avalanche strength and duration, and
transitions the power spectral density of the network into an `epileptic'
regime. We propose that the brain operates away from this power law regime of
low inhibitory fraction to protect itself from the dominating avalanches
present in these extended distributions. We present control strategies that
curtail these power law distributions through either random or, more
effectively, targeted disabling of excitatory neurons.
