In this paper, on condition that the word frequency follows the quasi power-law distribution and contents densification, it is proven that the Zipf’s law and Heaps law are equivalent, and critical behavior when γ=2 is also discussed.

Chinese air transport network’s time-varying and multi-layered featur are studieds by complex network theory. The results demonstrate that the three networks have similar features on degree distribution, short average path length, clustering coefficient, rich club coefficient, and assortativity coefficient, but the result of network similarity comparison demonstrates that the inner structures of the three networks are quite different. The transfer airline network will play important roles in optimization of the network structure.

It analyzed the interaction and impact between the networks by establishing the supernetworks of HMTN, and then the generating method of HMTN was established. It defined the concept of “the shortest path of HMTN”, “the average risk-path distance” and “the maximal connected subgraph”, proposed the “efficiency of network risk” and “maximal connected degree” as the measurement indexes of invulnerability model of HMTN. It established betweenness centrality model of HMTN according to its flow characteristic. Then the performance of invulnerability of HMTN was respectively researched. The simulation results show that: the invulnerability of HMTN is closer to the scale-free network which is robustness to random attack and vulnerability to deliberate attack; the invulnerability of HMTN is maintained by a small number of nodes and edges and the invulnerability of edge is higher than the node’s; the maximal connected degree of HMTN outperforms the efficiency of network risk and increase the redundancy of system appropriately can improve the invulnerability of HMTN.

To reveal the attack pattern, terrorism groups which attacked more than 500 events were empirically studied. Under the hypothesis that their interevent time follow power-law distribution, the maximum-likelihood estimation was applied to estimate the power-law exponent, and then the Kolmogorov-Smirnov（KS) statistic was used to test the hypothesis. The results show that the interevent time distributions of all the groups are power-law; The burst of terrorism attacks has no relationship with the foundation time and the lifetime; There is no positive correlation between average activity and power-law exponent and the group size is the main factor to affect it.

This paper establishes a multi-agent model on the spreading and governance of online negative word-of-mouth and examines the differences between the spreading and governance mechanism between regular network and small-world network. Simulation results show that the spreading and governance characteristics in different networks can be affected by the network size and structure, maturity of the community, etc.

In order to study the automobile cost transmission mechanism and strengthen cost forecasting and controlling of automotive industry, the paper transformed respectively the January 2001-November 2012 monthly price of crude oil （upstream), asbestos brake pads and auto parts（midstream), automobile sales （downstream) into symbolic sequences consisting of three characters （R, e, D) with symbolic dynamics. Monthly Symbol group is treated as nodes, connected nodes in chronological order, established automobile cost transmission synchronization complex networks of Guangzhou. The paper studied the degree distribution, the weighted clustering coefficient, average shortest path length, and community structure of network. The study found that peak intensity distribution followed the extension of exponential distribution. The average path length was 3.48, the conduction between nodes showed short-range correlation. The top 17 nodes in centrality measure play a key role of controlling the mode conversion, Major and minor nodes have a tendency to the normal node. The network is divided into three communities using Newman algorithms. The rise and decline trend play a very important role in the formation of associations.

To verify the reliability of the model in biology, we build a model of yeast protein interaction network according to the duplication-divergence model based on reported experimental data. The simulation results are greatly consistent with the real protein interaction networks especially on the acknowledged characteristic of sparsity, scale-free and small world. The duplication-divergence model shows its reliability to reproduce the evolution of protein interaction networks.

In this paper, we propose a novel centrality called connected dominating centrality according to the real-life demand analysis. The connected dominating set of a network has two characteristics, connectivity and dominance. Based on the two characteristics, we recursively construct the connected dominating sets of the induced dominating sub graphs and generate a directed spanning tree with dominating relationships. By combining the number of nodes dominated by a node, its hierarchical level in the directed spanning tree, and the weights of the edges which connect the dominator and its dominated nodes, we define the calculation formula of our proposed connected dominating centrality. To verify the effectiveness of the centrality, an experiment is made on the paper co-author network of an international journal. The experimental results show that the nodes with higher connected dominating centrality constitute the backbone network and can maintain the shape of network well. Some of them bridge different research communities; others are the kernels of communities. They have good ability in organizing and controlling the network.

The substructure of stock network, e.g. community, is investigated based on the synchronization theory by utilizing the correlation matrix of time series of stock price fluctuation. Through the spectral analysis on the correlation matrix, it’s determined that the complicated community structure obviously exists in the stock network. Then, the clustering algorithm based on the synchronization theory incorporating with the Kuramoto model is used to dynamically identify the community structure, which suggests that the groups of stocks well agree with the taxonomy of stock market. We also apply the fast community detecting algorithm to verify the former results with respect to the same parametric constrains.

This article focuses on the evolution of the rapid rumor spread on the microblog and the key factors affecting the spread of rumors. Based on the model of infectious diseases, expanded the people to the five class （ignorant, infected, contacted, exhausted, resistant), add the coefficient of interest decay to the model, and the individual just can be forward the rumor once. To verify the validity of the model, we made the multi-agent simulation, and made comparison to the simulation data and the data from two real cases. We found the model can be fit reality well. Through simulation experiments, the coefficients of different factors were analyzed and found that the coefficient of interest decay, the first forwarding probability and the properties of small-world networks can significantly affect the evolution of the spread.

Based on the dynamical equation for the model presented in paper [3], this paper focuesd on the influence of resource investment on the sustainable utilization of the resources. The existence and the local stability of the positive equilibrium were investigated by the use of the nonlinear dynamics. Then the local bifurcations of fixed points were verified through the numerical simulation. Finally, the extension of current stock in which resource can be renewable （feasible domain) was given by global method.

To probe into the construction mechanism of container liner network, its characteristics is analyzed to find that the expected volume between nodes is a key factor which determines the construction of liner route. The gravity model for container liner network is constructed by connecting the node pair in expected volume order. Then an empirical study on the East Asian container liner network is made in which the port fitness index is calculated to construct a simulative network. The evolution result demonstrates that the connectivity is enhancing and the major topological characteristics in simulative network are approaching those in physical network along with adding of lines. Thus, the model is validated and can be applied in container shipping practice.

In the China interbank market, the transaction behaviors of banks are similar and the interbank borrowing is short of regulation, which may result in a big problem. Considering this problem, the present paper constructs a dynamical bank network model, and then studies the stability of the dynamical bank network system with unconstrained behavior and constrained behavior of the agents based on the method of computational simulation. The results show that unconstrained interbank borrowing behavior will increase the system risk of the bank system. Furthermore, when the bank system becomes unstable due to this unconstrained behavior, it is difficult for the central bank to improve the stability of the bank system by adjusting the money policy of the deposit reserve rate.

In the paper, we firstly find that the steel products warehouse-out of all the warehouses in the large-scale logistics base is characterized by burst and the warehouse-out inter-event time follow the power-law distribution with exponents close to 2.5. On the meanwhile, compared with the group behaviors, the individual behavior does not show the burst feature in logistics system. Further, we discuss the burst mechanism caused by the festival holidays and interior task scheduling. Finally, the paper uses the R/S method to analyze the amount of the warehouse-out and finds it obey fractional Brownian motion. The Hurst over 0.5 means that the present warehouse-out of the logistics base is not only affected by the market price, but also related to the amount of the past accumulated amount.

This paper studies the consensus problem of multiple agents with continuous-time second-order dynamics, where each agent can obtain its velocity at any time, and can only obtain its position relative to its neighbors at discrete times. Under the given controller, some sufficient and necessary conditions are established, which are further applied to formation control of multiple robots. Simulations are performed to validate the theoretical results.