2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125571We study the excitable Greenberg-Hastings cellular automaton model on scale-free networks. We obtained analytical expressions for no external stimulus and 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, and there exists a relation $F\propto r^α$ for the low-stimulus response, where Stevens-Hill exponent $α$ ranges from $α= 1$ in the subcritical regime to $α= 0.5$ at criticality. At the critical point, the range reaches the maximal. 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.submitted to Phys. Rev. EStatistical MechanicsDisordered Systems and Neural Networkstext