Synchronizability Analysis Of Three Kinds Of Dynamical Weighted Fractal Networks

In this paper, we study the synchronizability of three kinds of dynamical weighted fractal networks (WFNs). These WFNs are weighted Cantor-dust networks, weighted Sierpinski networks and weighted Koch networks. We calculated some features of these WFNs, including average distance (davg), fractal dimension (D(0)), information dimension (D(1)), correlation dimension (D(2)). We analyze two representative types of synchronizable dynamical networks (the type-I and the type-II). There are two indexes (lambda 2 and lambda(N)/lambda(2)) that can be used to characterize the synchronizability of the two types of dynamical network. Here, lambda(2) and lambda(N) are the minimum nonzero eigenvalue and the maximum eigenvalue of the Laplacian matrix of the network, respectively. We find that the larger scaling factor f, D(0), D(1), D(2) or d(avg) implies stronger synchronizability for the type-I dynamical WFNs.