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Abstract

The branching process is the minimal model for propagation dynamics, avalanches, and criticality, broadly used in neuroscience. A simple extension of it, adding inhibitory nodes, induces a much-richer phenomenology, including an intermediate phase, between quiescence and saturation, that exhibits the key features of “asynchronous states” in cortical networks. Remarkably, in the inhibition-dominated case, it exhibits an extremely rich phase diagram that captures a wealth of nontrivial features of spontaneous brain activity, such as collective excitability, hysteresis, tilted avalanche shapes, and partial synchronization, allowing us to rationalize striking empirical findings within a common and parsimonious framework.