Stability of dynamic brain models in neuropercolation approximation

In this paper, the basic building blocks of the intentional neurodynamics cycle are studied using probabilistic cellular automata. We apply the mean field neuropercolation model to describe the dynamics of coupled excitatory-inhibitory neural populations. The model exhibits a phase transition between a background point attractor and narrow-band (limit-cycle) behavior, depending of the choice of system parameters. Metastable dynamics near criticality is investigated. We show the existence of various regions with unstable and multiple stable equilibria. The results are relevant to modeling cognitive phase transitions observed in brains during awareness experience.