Collective dynamics in heterogeneous networks of neuronal cellular automata

We examine the collective dynamics of heterogeneous random networks of model neuronal cellular automata. Each automaton has b active states, a single silent state and r-b-1 refractory states, and can show `spiking' or `bursting' behavior, depending on the values of b. We show that phase transitions that occur in the dynamical activity can be related to phase transitions in the structure of Erclos-Renyi graphs as a function of edge probability. Different forms of heterogeneity allow distinct structural phase transitions to become relevant. We also show that the dynamics on the network can be described by a semi annealed process and, as a result, can be related to the Boolean Lyapunov exponent. (C) 2017 Elsevier B.V. All rights reserved