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 approximately r{alpha} for the low-stimulus response, where the Stevens-Hill exponent alpha ranges from alpha=1 in the subcritical regime to alpha=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 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.
Wu
An-Cai
AC
Institute of Theoretical Physics, Lanzhou University, Lanzhou Gansu 730000, China.
Xu
Xin-Jian
XJ
Wang
Ying-Hai
YH
D000465:Algorithms; D003198:Computer Simulation; D008954:Models, Biological; D020543:Proteome / Q000378:metabolism*; D015398:Signal Transduction / Q000502:physiology*
D020543:Proteome