Synchronizability analysis of three kinds of dynamical weighted fractal networks

Abstract

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 ([Formula: see text]), fractal dimension ([Formula: see text]), information dimension ([Formula: see text]), correlation dimension ([Formula: see text]). We analyze two representative types of synchronizable dynamical networks (the type-I and the type-II). There are two indexes ([Formula: see text] and [Formula: see text]) that can be used to characterize the synchronizability of the two types of dynamical network. Here, [Formula: see text] and [Formula: see text] are the minimum nonzero eigenvalue and the maximum eigenvalue of the Laplacian matrix of the network, respectively. We find that the larger scaling factor [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] or [Formula: see text] implies stronger synchronizability for the type-I dynamical WFNs.

The average trapping time of non-nearest-neighbor jumps on nested networks

“…The diffusion efficiency is inversely proportional to the value of ATT, that is, the smaller the ATT, the higher the diffusion efficiency of the network; the larger the ATT, the lower the diffusion efficiency of the network. Relevant scholars have studied the trapping problem in triangle network [17], crystal network [22], flower network [23,24], ring tree network [25,26], fractal network [27], SG network [28], etc., and obtained the analytical formula of ATT. The walking style of these problems considers a simple random walk, that is, moving from a node to its nearest neighbor (NN) node.…”