Synchronizabilities of Networks: A New index

The random matrix theory is used to bridge the network structures and the dynamical processes defined on them. We propose a possible dynamical mechanism for the enhancement effect of network structures on synchronization processes, based upon which a dynamic-based index of the synchronizability is introduced in the present paper.Comment: 4pages, 2figure

Scaling Invariance in Spectra of Complex Networks: A Diffusion Factorial Moment Approach

A new method called diffusion factorial moment (DFM) is used to obtain scaling features embedded in spectra of complex networks. For an Erdos-Renyi network with connecting probability $p_{ER} < \frac{1}{N}$, the scaling parameter is $\delta = 0.51$, while for $p_{ER} \ge \frac{1}{N}$ the scaling parameter deviates from it significantly. For WS small-world networks, in the special region $p_r \in [0.05,0.2]$, typical scale invariance is found. For GRN networks, in the range of $\theta\in[0.33,049]$, we have $\delta=0.6\pm 0.1$. And the value of $\delta$ oscillates around $\delta=0.6$ abruptly. In the range of $\theta\in[0.54,1]$, we have basically $\delta>0.7$. Scale invariance is one of the common features of the three kinds of networks, which can be employed as a global measurement of complex networks in a unified way.Comment: 6 pages, 8 figures. to appear in Physical Review

Collective Chaos Induced by Structures of Complex Networks

Mapping a complex network of $N$coupled identical oscillators to a quantum system, the nearest neighbor level spacing (NNLS) distribution is used to identify collective chaos in the corresponding classical dynamics on the complex network. The classical dynamics on an Erdos-Renyi network with the wiring probability $p_{ER} \le \frac{1}{N}$ is in the state of collective order, while that on an Erdos-Renyi network with $p_{ER} > \frac{1}{N}$ in the state of collective chaos. The dynamics on a WS Small-world complex network evolves from collective order to collective chaos rapidly in the region of the rewiring probability $p_r \in [0.0,0.1]$, and then keeps chaotic up to $p_r = 1.0$. The dynamics on a Growing Random Network (GRN) is in a special state deviates from order significantly in a way opposite to that on WS small-world networks. Each network can be measured by a couple values of two parameters $(\beta ,\eta)$.Comment: 15 pages, 12 figures, To appear in Physica