Phase synchronization on scale-free and random networks in the presence of noise

In this work we investigate the stability of synchronized states for the Kuramoto model on scale-free ( SF) and Erdos-Renyi ( ER) random networks in the presence of white noise forcing. We show that for a fixed coupling constant, the robustness of the globally synchronized state against the noise depends on the noise intensity on both kinds of networks. At low noise intensities ER networks are more robust against losing the coherency but upon increasing the noise, synchronization among the population vanishes suddenly at a specific noise strength. In contrast, on SF networks the global synchronization disappears continuously at a much larger critical noise intensity with respect to ER networks.