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The Wilson-Cowan model constitutes a paradigmatic approach to understandingthe collective dynamics of networks of excitatory and inhibitory units. It hasbeen profusely used in the literature to analyze the possible phases of neuralnetworks at a mean-field level, e.g., assuming large fully-connected networks.Moreover, its stochastic counterpart allows one to study fluctuation-inducedphenomena, such as avalanches. Here, we revisit the stochastic Wilson-Cowanmodel paying special attention to the possible phase transitions betweenquiescent and active phases. We unveil eight possible types of phasetransitions, including continuous ones with scaling behavior belonging to knownuniversality classes -- such as directed percolation and tricritical directedpercolation -- as well as novel ones. In particular, we show that under somespecial circumstances, at a so-called Hopf tricritical directed percolationtransition, rather unconventional behavior including an anomalous breakdown ofscaling emerges. These results broaden our knowledge of the possible types ofcritical behavior in networks of excitatory and inhibitory units and are ofrelevance to understanding avalanche dynamics in actual neuronal recordings.From a more general perspective, these results help extend the theory ofnon-equilibrium phase transitions into quiescent or absorbing states.

Unconventional criticality, scaling breakdown, and diverse universality classes in the Wilson-Cowan model of neural dynamics