We study a neural network model of interacting stochastic discrete two-state cellular automata on a regular lattice. The system is externally tuned to a critical point which varies with the degree of stochasticity (or the effective temperature). There are avalanches of neuronal activity, namely, spatially and temporally contiguous sites of activity; a detailed numerical study of these activity avalanches is presented, and single, joint, and marginal probability distributions are computed. At the critical point, we find that the scaling exponents for the variables are in good agreement with a mean-field theory.
Kaustubh Manchanda, Avinash Chand Yadav, and Ramakrishna Ramaswamy
"Scaling behavior in probabilistic neuronal cellular automata"
Phys. Rev. E 87, 012704 (2013)