Empirical evidence suggests that cortical networks operate near a continuous phase transition, conjectured to be an optimum for information storage and processing. Applying theoretical approaches, however, is challenging since vital features of neural networks present numerous obstacles to the applicability of traditional statistical physics tools, many of which have not yet been adapted to neuroscience. I describe a simple cellular automaton model which allows for the characterization of nonequilibrium transitions and demonstrates an explicit symmetry breaking due to external stimuli. The resulting quasicriticality theory predicts that cortical networks operate in a crossover region, where critical exponents vary along a nonequilibrium Widom line while still agreeing with fundamental scaling relations, and a rich phase diagram with dynamical transitions which may correspond to epileptic phases. Examination of this oscillatory phase in the model reveals evidence of unusual routes to chaos and soliton waves traversing the state space, potentially opening doors to a field theory. Further development of these tools help our understanding of brain dynamics.
Maxim Chernodub
