The spacing of nearest levels of the spectrum of a complex network can be regarded as a time

By means of the concept DE we analyze the responses of a HH neuron to two types of spike-train inputs. Two characteristic quantities can be extracted, which can reflect partially the dynamical process of a HH neuron.

By means of the concept of Factorial Moments we examine DNA sequences from Yeast to distinguish coding and non-coding regions. It is found that the FM may be a powerful tool for analysis of DNA sequences. PACS numbers: 87.15.Cc,87.10.+e,87.14.GgComment: 10pages, 2figure

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 ≤ 1 N is in the state of collective order, while that on an Erdos-Renyi network with p ER > 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 ∈ [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 (β, η).

A new method called diffusion factorial moment is used to obtain scaling features embedded in the spectra of complex networks. For an Erdos-Renyi network with connecting probability p(ER) < 1/N, the scaling parameter is delta = 0.51, while for p(ER) > or = 1/N the scaling parameter deviates from it significantly. For WS small-world networks, in the special region p(r) element of [0.05,0.2], typical scale invariance is found. For growing random networks, in the range of theta element of [0.33,049], we have delta = 0.6 +.- 0.1. And the value of delta oscillates around delta = 0.6 abruptly. In the range of delta element of [0.54,1], we have basically element of > 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.