  We propose that a regulation mechanism based on Hebbian covariance plasticity
may cause the brain to operate near criticality. We analyze the effect of such
a regulation on the dynamics of a network with excitatory and inhibitory
neurons and uniform connectivity within and across the two populations. We show
that, under broad conditions, the system converges to a critical state lying at
the common boundary of three regions in parameter space; these correspond to
three modes of behavior: high activity, low activity, oscillation.
