In this Review, we mainly focus on solving the threshold theoretically, and introduce seven common methods, including Mean-Field theory, Pair-wise Approximation, Master equation, Generating Function, Edge Percolation, Cavity method, Edge Classification and Spectral analysis. We also summarize the difference of thresholds between the SIS and SIR model. We are aiming to provide a clear picture for beginners and a good reference for researchers

In this paper, a brief review of the theoretical framework of a single network picture is given; Overview of the current concern of the "network of networks" or super network, the related definitions and concepts, introduction to several theory model of multilayer super network research, finally puts forward ten challenging tasks to network science.

For a long time, spreading dynamics is a very important subject in network science. Recent studies on the spreading dynamics on the multilayer coupled networks attract attention both at home and abroad. This review article introduces the progress of spreading dynamics on the multilayer coupled networks and some open questions, mainly focusing on the following four aspects: (1) biological spreading on the multilayer coupled networks; (2)social contagion on the multilayer coupled networks; (3) biological-social coupling transmission on the multilayer coupled networks; and (4) some problems on multilayer coupled networks. These episodes of research from a new angle of multilayer coupled network deepened our understanding of the real propagations. The problems discussed here will help to clear the direction of next stage

In this article, a review on recent progress of related fields is given, based on the robustness of multilayer networks, the Laplacian spectra of multilayer networks, the time pattern of temporal networks, the opinion dynamics on multilayer networks and temporal networks.

We propose a model to quantify long-term scientific impact and obtain analytic results of the model. It is more reasonable than the model proposed by Barabási et al. The total citation count of a paper in its life cycle represents its long-term scientific impact. The results show that the value is only related to the paper’s fitness. It means that the content and the quality of the paper represents, the capability of its competitiveness, and determine its long-term impact.

This paper first analyzes the terrorist groups from the individual to the group, the development of the group to the network, in secondely, was proposed and constructed a model of a terrorist group network;Third, evolution process of the terrorism group network has analyzed; And the movement of one of the most simple model of dynamic equation and its features. Finally, put forward and the profile of network control method of terrorist organizations.

In this paper, an overview of vaccination methods addressing in suppressing the epidemic spreading is given, focusing on modeling the epidemic and public sentiment spreading from real world scenarios, describing models of dynamic spreading, and presenting vaccination strategies and their efficiency. Simulation results on empirical networks and model networks using different vaccination strategies show that vaccination strategies such as centrality-based vaccination, graph partition-based vaccination and acquaintance vaccination are more effective than random vaccination. This implies that vaccination strategy is important and meaningful in suppressing epidemic spreading. In order to reach a better control result, the topological structure and the completeness of network information should be taken into account when choosing a vaccination strategy.

Unifying hybrid theory network model (UHNTF) has more abundant topological characteristics and can be used to analyze and study many practical networks, so the research of multilayer supernetwork model based on UHNTF has theoretical value and practical significance. For this reason, UHNTF is combined with supernetwork feature in this paper. We proposed four kinds of supernetwork models, calculated and analyzed the relationship between hybrid ratios and topological characteristics. Some new features are found and the results can help to understand evolution of supernetwork model under different connecting pattern, which provide certain theoretical basis for research and potential application.

This paper initiates a novel approach to generate multi-wing butterfly attractor from the Liu chaotic system. The main idea is to increase the number of index-2 saddle-focus of chaotic system. By substitution of multi-segment quadratic function, the Liu′s chaotic system is designed to create many index-2 saddle-focus and generate multi-wing butterfly attractor. Theoretical analysis shows that every index-2 equilibrium point corresponds to unique wing in the butterfly attractor. The simulation demostrates the feasibility and effectiveness of the proposed method.

This paper constructs the empirical network of the clonal plant multiple relation treelike networks based on the spatial configuration of Spartina alterniflora to explore the evolutionary game characteristics. First, we study the structure properties of Spartina alterniflora, which reflect the ecological strategy that avoiding competition between each other. Second, the model of the evolutionary Prisoner’s Dilemma game is introduced into the Spartina alterniflora treelike network. Initially, the distribution of strategies among the nodes in the network obeys two different rules: distributed randomly, with f_c decreasing with the increasing of b, in accordance with different types of Spartina alterniflora biological units, the rhizome nodes between the neighboring bunches play an important role.

The algorithms of detecting community in complex networks now have lots of disadvantages such as high complexity and ignorance of accurate overlapping nodes. This paper proposes a highly efficient, rapid and accurate community detection algorithm. Based on greedy algorithm, the community is divided by establishing the modularity matrix and adopting the data structure. Considering the edges between local communities, the overlapping community structure is accurately dug by computing the partition density. We evaluate our methods using both synthetic benchmarks and real-world networks, demonstrating the effectiveness of our approach. Our method runs in essentially linear time.

In order to investigate the distribution pattern of investigation scope and decision threshold of spies when introduce spy agents into the minority game model, we investigate different situations with different spy number proportions. Spies take the principle "win stay, lose move" to adapt their investigation scope or decision threshold. It was found that when spy number is small, the proportion of large investigation scope is in the majority; yet when spy number is large, the proportion of small investigation scope is in the majority. When investigation scope is small, spy prefer to adopt half decision threshold; yet when investigation scope is large, the distribution scope of decision threshold of different spies is widespread.