The Complexity Study is a new field in the Science. It provided a new thingking approach for researchers. The Trandisional Thingking, as its typical represantive, the Newtonian Mechanics, always ignored the complexity of real world. The main shortage of tranditinal thinking is oversimplification, absolute thinking and ignore the role of time. The Complexity Study paid more attention on the complexity of the world.What caused the Complexity? How to deal with the Complexity? From six different perspectives, this paper provided a framwork for understanding the Complexity. The six perspectives are: the Vergeness of Convepts, Quantitive Diversity, Multi-perspectives, Hierarchy feature, Role of the Time, Role of the Information. Complexity is not a new Grant Narrative, it has rejected any final theoritical frame, instead it provided further direction for understanding the complexity and further exploration.

In this paper, research status quo on the cascading vulnerability of interdependent networks is reviewed firstly. Secondly,its progress and unsolved problem are analyzed.Based on this,the blind area of the present interdependent networks vulnerability research—correlation mechanism and correlation principle of interdependent networks are deeply analyzed and studied,and the vulnerability analysis models which based on the correlation degree distribution functions are built,at the same time,six criteria of interdependent networks vulnerability evaluation are summed up.Lastly,the conclusion and proposal are put forward.

For resolving the contradiction between power-law distribution playing an increasingly important role in investigation of complex systems and it has not been derived out up to now, in this paper the maximal entropy principle and the idea of incomplete statistics were utilized. Firstly, the detail of deriving the equal probability hypothesis from Shannon entropy and maximum entropy principle was showed. Then three different exponential factors were introduced in equations about the normalization condition, statistical average and Shannon entropy respectively. Based on the Shannon entropy and maximum entropy principle, three different probability distribution functions, such as exponential function, power function and the product form consisting of power function and exponential function, were derived out. Which demonstrated the maximum entropy principle was a path which may lead to different distribution functions.

Considering the high concentration, scale-free and “community structure” of social networks, according to “Prisoner's Dilemma” game, we establish an evolutionary game model for complex social networks based on multi-preferences, apply the node influence to the rule of game strategy update innovatively, and use Matlab platform to simulate. Besides, we analyze the multi-preferences, “community structure” and inter-community links to reveal the influence and inherent mechanism of cooperative emergence in social networks systematically from both macroscopic and microcosmic perspective through contrast simulation experiments. It is shown that community structure characteristic under multi-preferences affects the heterogeneous expectation level of agents; “community structure” can promote the emergence of cooperation; the influence of inter-community links to cooperative emergence has a relation with community scale.

Complexity is defined to describe the partial synchronization state in complex networks, which is sensitive to the network structure, however, how the structure affects the complexity is still unclear. Clustering coefficient and degree distribution are two typical parameters in complex networks. In this paper, the effects of these two parameters on complexity are studied. After careful study it is found that increasing clustering coefficient would increase the maximal complexity and broaden the width of the complexity curves, and increasing the heterogeneity of the degree distribution will increase the value of rising and falling part of complexity curve but have no effect on the maximal complexity. Furthermore, complexity is sensitive to clustering coefficient in small-world networks and sensitive to heterogeneity of degree distribution in scale-free networks. Our work deepens the knowledge of complexity, and provide useful theory to design complex network structure.

This paper presents a new method for security analysis and precautionary measures when attack or error occurs in networks. This method describes the operating region under N-1 constraint and presents the degree of security or insecurity by secure distance to indicate direction and intensity for next step. We put the method into effect in general networks, small communication network and large-scale power network to verify its correctness, and compare it with network invulnerability. It can be seen that secure distance index and invulnerability index are very consistent in judging the reliability of a system, meanwhile, the former can bring secure region information to eliminate hidden dangers in advance and be appropriate for online security surveillance and control based on faster calculation speed.

An evolving hypernetwork model is constructed with both preferential and random attachment. We analyze the model by using Poisson process theory and a continuous technique, and obtain the stationary average hyperdegree distribution of the hypernetwork. The analytical result shows that the stationary average hyperdegree distribution can be described with “shifted power law” (SPL) function form. Our model is also universal, in that the standard model in complex networks and scale-free model in hypernetworks can all be seen as degenerate cases of the model. By adjusting the parameter, the model can reflect the mixed-connection mechanism. In addition, three empirical data are analyzed, and can be effectively described by the model.

This paper gives the definition of node’s dynamic connection degree at first, and then introduces the algorithm of finding the community structure by the node’s dynamic connection degree. After that, it analyzes the range of parameter’s value in node’s connection degree and proves it by experimenting on the Zachary network. On this basis, it experiments on three real networks which are dolphins, polbooks and football. The result proves that this algorithm can find different network’s community structure correctly by adjust its parameter’s value. At last, it compares the result with some other common algorithms’ and illustrates some matters that need attention.

Based on the topology feature of networked systems, maximum synchronization of distributed systems is studied. A distributed control protocol with individual′s local information is proposed. By using theoretical tools of modern control theory, algebraic graph theory and SIA, the stability of control algorithm is analyzed. The convergence condition of the maximum synchronization for networked systems is achieved. Finally, simulation examples are given to verify the correctness of the conclusion.

This paper integrates input-output model with agent-based simulation, in which an input-output model with 17 sectors is established at the macro economy level, and an agent-based model is developed simulating firms’ innovations in each sector at the micro economy level. The emergency of industrial structure evolution,energy consumption change and carbon emission change at the macro level are driven by innovations of firm agents. Results show that due to the uncertainty of innovation, the peak years of energy and emission are also uncertain. The energy peak year will subject to a normal distribution from 2025 to 2036; while the distribution of emission peak year is also identified as a normal distribution from 2024 to 2033. The year with the maximum probability for energy peak will be 2031 with the probability of 23.57%; and 2029 will be the year with the maximum probability 33.51% for emission peak. Taking the average of 50 simulations, it is indicated that the energy peak will be 5146Mtce in 2029, and the emission peak will be 2.7GtC in 2029.

In this paper, a R&D input game model with spillovers, endogenous demand in a triopoly market is considered. All the players only get incomplete information and we assume they are all bounded rational. Two players make up a cooperative team, and share the technology achievements completely. On the basis of analyzing the stabilities of the only Nash equilibrium point, three-dimensional stable regions are investigated. The complex dynamics, such as bifurcation scenarios, route to chaos are displayed by 2D bifurcation diagrams. Impact of the adjustment speed, spillover rate and endogenous demand parameter on the profit is studied.

In this paper, we present an innovation diffusion model based on the local interaction and global broadcasting, which considers both the interaction between each node and the influence of the public media during the innovation spreading process. The experimental results show that as the effect of the global broadcasting is limited, the local interaction relationships would play an important role in the innovation diffusion. Furthermore, the simulation results on for real networks show that under the limited influence of public media, the improved method which integrates the network structure and innovation diffusion process can evaluate the node influence in innovation diffusion accurately. Comparing with degree, closeness and K-shell method, the largest improved ratio could reach 39.19%, 35.61% and 33.03% respectively.

Prisoner’s dilemma is an important tool to study the adaptation of cooperative strategies. Individuals can maximize their profits by cooperating with each other. In this paper, the method of ecological simulation is adopted to study the effects of noise and interaction frequency on the evolution of cooperative strategies in the context of the Noisy Iterated Prisoner’s Dilemma (NIPD), a version of the Iterated Prisoner’s Dilemma (IPD). The results illustrate that noise and interaction frequency are important factors to the surviving strategies.

A consensus problem is discussed about the second-order multi-agent system with multiple time-varying input delays.Firstly,by variable transformution,the convergence problem of second-order multi-agent systems is converted into the stability problem of an error system.Then,by system transformution,the stability problem of the second-order system is converted into the stability problem of the equivalent system. Based on linear matrix inequalities (LMI),by constructing Lyapunov-Krasovskii functions,sufficient conditions of consensus in undirected networks are obtained. At last,examples are given to demonstrate the effictiveness of the conclusion.