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∼r^α 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 F^k(r) and the dynamic range Δ^k(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.