Synchronization of delayed fluctuating complex networks

In this communication we present some of our recent results on the synchronization properties of directed delay-coupled networks of a small-world type, whose topology changes with time. Our simulations of a network of non-linear elements show that a random change of topology enhances the stability of a synchronized state, depending on the interplay between different time-scales in the dynamics. The results are analytically explained in the linear limit, where the dynamics is expressed in terms of an effective connectivity matrix. In the limit of fast network fluctuations, this effective connectivity is given by the arithmetic mean of the temporal adjacency matrices. When the coupling topology changes slowly, the effective adjacency matrix is given by the geometric mean. The transition between both regimes is numerically studied for linear network elements.