Mean Field Theory for Generalized Cortical Branching Model

The brain is a complex, far-from-equilibrium dynamical system consisting of diverse populations of neurons and neurotransmitters. One of the interesting behaviors observed in the mammalian brain are neuronal avalanches, which are partly explained by the Cortical Branching Model (CBM), a many-body model consisting exclusively of excitatory neurons. Here, we develop a generalized CBM (GCBM) to incorporate inhibitory neurons and their varied motifs of interaction. To gain understanding and predict behavior of this many-body system, we develop a method to generate mean-field approximations for any given motif with or without inhibition. This mean-field theory allows us to produce dynamical maps from basic interactions among excitatory and inhibitory neurons, from which it will be possible to study corresponding phase diagrams and nonequilibrium phase transition of the GCBM.