Are sparse all scale-free networks?Is the sub-network of randomly sampling from a scale-free network is scale-free? Whether degree exponent of Apollonius network need to add 1? This paper uses our definition and classification of scale-free network, and definition of degree exponent to give analysis of causes to dispute and the correct answer.

Taking into account the differences between individual immune to rumours on real-world complex networks, to describe non-uniform propagation rates of different nodes by introducing the rumour acceptability function. Based on mean-field theory, rumour propagation model for scale-free network with non-uniform propagation rates was proposed, and then the behavior of rumour propagation on scale-free network was studied. Theoretical analysis and simulation results show that nodes with different rumour acceptability could lead to slowing the spread of rumours. Furthermore, rumour acceptability make positive propagation threshold arise, and effectively contain the outbreak and reduce the risk of rumours.

Cascading failure model for single layer network can’t be used to analyse the invulnerability of layered networks effectively. Based on betweenness analytical method, this article studies the cascading failure model for double layer complex networks. Firstly, it analyses interaction between the two layers when the network is in state of common information （or energy) exchanging or in course of cascading failure. Secondly, by defining parameter of communicating intensity, algorithm of node betweenness is amended, so that affection of node function to network flux could be validated. And then, by resetting rules of node failure judging and load re-allotting, the two layers are associated in course of cascading failure. At last, through simulation experiments, effectiveness and maneuverability of the model is verified.

Based on the previous studies on pedestrian evacuation with limited visibility, an advanced evacuation model is proposed using the cellular automata theory; and the evacuation time with and without evacuation sign is estimated. Using computer simulation, the influence factors of pedestrian evacuation are studied from the evacuation time and the use ratio of exit . The results show that exit signs have an obvious effect on improvement of evacuation efficiency, which avoids the phenomenon of pedestrian bypass. Evacuation time gradually decreases with the increase of visible distance and visual range of exit signs, but the corresponding and the use ratio of exit shows the opposite variation trend. The evacuation time and the use ratio of exit decrease with the increase of the exit width. Meanwhile, the optimal evacuation conditions are explained using two factors which are the evacuation time and the use ratio of exit, which is that when the short evacuation time is satisfied, the use ratio of exit should be also high.

We introduce the concept of m-order neighbors and propose an evaluation method of vital node for complex networks based on importance contribution of m-order neighbors.Two parameters α and γ are defined for adjusting the dependences of node importance evaluation on the node itself and m-order neighbors. This method considers the importance contribution of the node itself and m-order neighbors. In order to characterize the efficiency of this method, ARPA network is adopted to evaluate the node importance with different values of m. The results shows that, compared with the degree method, betweenness method and node deletion method, our algorithm is more precise to evaluate the node importance, which can observably distinguish the importance discrepancy of the nodes on the complex networks and precisely extract the vital nodes. Meanwhile, the results also reveal an important dynamic phenomenon that when the value of m is more than the average path length L of the network, our method can derive reliable and high precise evaluation results.

Since many real networks generally have community structures and characteristics of small world, we propose a dynamical small-world network model with strength-tunable community, which can describe the phenomena of local contacts and moving contacts in real life. Then we construct a SIR transmission model on the proposed network on the basis of mean-field theory. Simulations and analysis show that, with the increase of inter-community long range jump probabilities, the epidemic threshold will decrease. And the larger the community strength is, the larger the epidemic threshold will be. Namely, large community degree can reduce the spreading of the virus. Additionally, in order to suppress the epidemic spreading, it is effective to strengthen the control of inter-community long range jump.

The model assumes that new and remanufactured products have different market prices, based on this we established the dynamic decision model between the manufacturer and the recyclers; using numerical simulation, bifurcation diagram, maximum Lyapunov index dynamic variation diagram and attractor to study the complexity character of the system; analyzing the initial value sensitivity of the system; and at last we controlled the chaos of the system successfully. The conclusions that chaos reduces profit remarkably and chaos can be controlled have useful guiding significance.

The complex network is established to measure correlations in fluctuation among index return series of stock markets from various countries, with the Kendall’s τ rank correlation coefficient as the edge weight. The network topology characteristics are studied and analysis results show that the international stock market network is endowed with small-world effect, without scale-free nature and three communities are found. The results agree with reality,which has certain instructive effect on the setting of immunization strategies.

Externality is an essential factor in the formulation and evolution of eco-industrial symbiosis network. With considering the externality, we study the co-opetition relationship between the producer enterprises and decomposer enterprises in EISN, and by conducting the corresponding evolutionary game model and replicator dynamic equation, the impact of externality on the evolution and long-term equilibrium of EISN under imperfect and bounded rationality is analyzed. The result shows that the long-term equilibrium of the EISN is affected by the initial state of the game occurring, the expectation of the external effect benefits, the payment cost to choice the cooperative strategy and the discount factors when taking the externality into consideration. Finally, taking the Lubei eco-industrial park as the case, we verify the conclusions by numerical examples and propose some valid suggestions.

On the basis of dynamic oligopoly game models, in which price is the only decision variable, we creativity introduce product quality level as a new decision variable in this paper to meet the actual circumstances better, and a new dynamic duopoly game model with dual decision variables was established under the consideration of bounded rationality. Firstly, we analyze the complexity of this model as well as four kinds of equilibrium points. Secondly, system properties are showed by numerical simulation. We can find that adding a new variable can reduce the stable region as well as increase profit, and two kinds of bifurcations are corresponding similar and the influence of each parameter on total profit and on stability domain are mostly in opposite directions. These studies have theoretical and practical values to guide the behaviors of dynamic oligopoly game with dual decision variables.

We establish a staged progression epidemic model on complex networks. With the analysis of dynamical behavior, the basic reproduction number and final size are obtained. We discover that the early stage patients can intensify the disease when it is spreading on the heterogeneous networks. The correctness of our theoretical results are validated by numerical simulations.

To better explore the robustness against cascading failures on complex networks, a local congestion-aware routing strategy with a tunable parameter is proposed,and a cascading model is constructed. According to new measures to the robustness of a network against cascading failures, cascading behaviors on complex heterogeneous networks triggered by deliberate attacks are investigated. Simulation results show that, under the local routing, the existence of an optimal value of the routing parameter makes the networks achieve a maximum level of robustness and, the robustness of the networks has a negative correlation with time delay of congestion information and the network size respectively. Moreover, compared with a global routing, the local routing makes the networks more robustness when the packet generation is large.

Used the method of social network analysis,construct the scientific collaboration network of authors, which formed during the period 2004 to 2013. Further more, compare the cha-racteristic of several larger interior connected sub-networks, analyze the forming reasons of network characteristic and the impact of author collaboration. Analysis data show that the author collaboration network is a non-connected network of network characteristic of scale-free and small world. Statistical data also show that scientists who are the central nodes in the collaboration networks, can bring the development of academic exchange in scientific research units and the deve-lopment of scientific work.