  For the nervous system to work at all, a delicate balance of excitation and
inhibition must be achieved. However, when such a balance is sought by global
strategies, only few modes remain balanced close to instability, and all other
modes are strongly stable. Here we present a simple model of neural tissue in
which this balance is sought locally by neurons following `anti-Hebbian'
behavior: {\sl all} degrees of freedom achieve a close balance of excitation
and inhibition and become "critical" in the dynamical sense. At long
timescales, the modes of our model oscillate around the instability line, so an
extremely complex "breakout" dynamics ensues in which different modes of the
system oscillate between prominence and extinction. We show the system develops
various anomalous statistical behaviours and hence becomes self-organized
critical in the statistical sense.
