  We 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 $F\propto r^\alpha$ for
the low-stimulus response, where Stevens-Hill exponent $\alpha$ ranges from
$\alpha = 1$ in the subcritical regime to $\alpha = 0.5$ at criticality. At the
critical point, the range reaches the maximal. We also calculate the average
activity $F^{k}(r)$ and the dynamic range $\Delta^{k}(p)$ 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.
