  Recent experiments suggested that homeostatic regulation of synaptic balance
leads the visual system to recover and maintain a regime of power-law
avalanches. Here we study an excitatory/inhibitory (E/I) mean-field neuronal
network that has a critical point with power-law avalanches and synaptic
balance. When short term depression in inhibitory synapses and firing threshold
adaptation are added, the system hovers around the critical point. This
homeostatically self-organized quasi-critical (SOqC) dynamics generates E/I
synaptic current cancellation in fast time scales, causing fluctuation-driven
asynchronous-irregular (AI) firing. We present the full phase diagram of the
model without adaptation varying external input versus synaptic coupling. This
system has a rich dynamical repertoire of spiking patterns: synchronous regular
(SR), asynchronous regular (AR), synchronous irregular (SI), slow oscillations
(SO) and AI. It also presents dynamic balance of synaptic currents, since
inhibitory currents try and compensate excitatory currents over time, resulting
in both of them scaling linearly with external input. Our model thus unifies
two different perspectives on cortical spontaneous activity: both critical
avalanches and fluctuation-driven AI firing arise from SOqC homeostatic
adaptation, and are indeed two sides of the same coin.
