Synchronization on Erdös-Rényi networks

In this Brief Report, by analyzing the spectral properties of the Laplacian matrix of Erd\"os-R\'enyi networks, we obtained the critical coupling strength of the complete synchronization analytically. In particular, for any size of the networks, when the average degree is greater than a threshold and the coupling strength is large enough, the networks can synchronize. Here, the threshold is determined by the value of the maximal Lyapunov exponent of each dynamical unit.