Balanced excitation and inhibition lead to statistical and dynamical criticality

We present a simple abstract model, an anti-Hebbian network which spontaneously poises itself, by balancing excitation and inhibition, at a dynamically critical state: an extensive number of degrees of freedom approach Hopf bifurcations, becoming arbitrarily sensitive to external perturbations (PRL~102, 258102 - 2009). As the dynamics controlling this state has itself a marginal fixed point, the eigenvalues fluctuate close to the imaginary axis; when they become slightly unstable, the corresponding mode ``breaks out'' and becomes more prominent, and as they become slightly stable the mode slowly damps out. This breakout dynamics displays avalanche-like activity bursts whose sizes may be power-law distributed, i.e. statistically critical. Within these epochs the neurons of our model are slightly correlated; yet, as the number of small but significant correlations is high, the model has strongly correlated network states. This system is, on the short time-scale, sensitive in bulk to any outside input, even if applied only to a small subset of the neurons. We also present preliminary results showing that human brain electro-physiological recordings display both statistical and dynamical criticality.