Quasicriticality: On the brink of phase transitions and chaos in the cortex

The mean-field approximation of the cortical branching model produces a rich phase diagram featuring a number of dynamical transitions indicative of different situations depending on parameter values. One such transition features a shift from convergence to a stable fixed point (an ordered phase), to limiting quasiperiodic oscillations. This quasiperiodic phase may correspond to neurological disorders such as epilepsy and features evidence of unusual routes to chaos, soliton excitations, and a reentrant regime at extreme parameter values. An analytic expression of the mean-field approximation may be possible in this regime via correspondence with a dispersive PDE (e.g., the Kordeweg-de-Vries equation), potentially opening doors to a field theory of complex neural networks.