Synchronization in Generalized Erdös-Rényi Networks of Nonlinear Oscillators

In this paper, we study synchronization of complex random networks of nonlinear oscillators, with specifiable expected degree distribution. We review a sufficient condition for synchronization and a sufficient condition for desynchro- nization, expressed in terms of the eigenvalue distribution of the Laplacian of the graph and the coupling strength. We then provide a general way to approximate the Laplacian eigenvalue distribution for the case of large random graphs produced by a generalization, (2), of the Erd¨´ enyi model. Our approach is based on approximating the moments of the eigenvalue density function. The analysis is illustrated by using a complex network of nonlinear oscillators, with a power-law degree distribution.