Excitable Greenberg-Hastings cellular automaton model on scale-free networks

We study the excitable Greenberg-Hastings cellular automaton model on scale-free networks. We obtain analytical expressions for no external stimulus the uncoupled case. It is found that the curves, the average activity F versus the external stimulus rate r, can be fitted by a Hill function, but not exactly, there exists a relation F∼ rα for the low-stimulus response, where the Stevens-Hill exponent α ranges from α=1 in the subcritical regime to α=0.5 at criticality. At the critical point, the range is maximal, but not divergent. We also calculate the average activity Fk (r) and the dynamic range Δk (p) for nodes with given connectivity k. It is interesting that nodes with larger connectivity have larger optimal range, which could be applied in biological experiments to reveal the network topology.