Optimizing the synchronizability of generalized deactivation networks

We research the synchronizability of the generalized deactivation networks without changing its degree distribution. The synchronizability measured by the eigenratio R can be effectively optimized by adjusting the only parameter, the number of active nodes M. The eigenratio R is shown very sensitive to the M, and larger M will lead to better synchronizability. Furthermore, we find that, in a wide interval, the eigenratio R obeys a approximate power-law in the form of R similar to M-2.0. By introducing a perturbation, the synchronizability of network can be effectively optimized.