The conditions for the spontaneous emergence of cooperation under the complex human behavior model have become the focus of many disciplines. Exploring the conditions for cooperation has both important scientific significance and theoretical value for understanding the institutional arrangements in human society. The social dilemma games provide a theoretical prototype for studying cooperation issues between multiple individuals. As a dynamic analysis method that can describe individuals′ learning and strategy adjustment processes, evolutionary game theory has been one of the most effective frameworks for studying the evolution of cooperation. This review article systematically summarizes the research progress of using the evolutionary game method to study the issues of group cooperation in social dilemma games. Specifically, the following topics are included: research progress of (1) social dilemma game models, evolutionary game theory and equilibrium analysis methods, (2) social dilemma games and the evolution of cooperation under reward/punishment mechanism and reputation mechanism, (3) social dilemma games and the evolution of cooperation with separation strategy and extortion strategy, and (4) social dilemma games and the evolution of cooperation under the network reciprocity. Finally, prospects for further research issues in this area are presented.

Reviews and prospects the existing academic literature in terms of research paradigms, research methods and research tools on the complexity of international capital flow network. Studies show that the research paradigm ofcomplexity science based on discrete spatial network is pretty suitablefor the research on the complexity of international capital flow network. And the procedure, consisting of "construction of complex discrete network—system evolution—relationship analysis on input and output—proposals fordecision making ", can work quite well while doing this research. Besides, the construction and topological structure analysis of international trade capital flow network, which also belongs to international fund interactive network, could be applied to the research on the complexity of international capital flow network in the context of increasing data availability. And after the expansion on network node and neighbor mode, the newly defined generalized cellular automaton model could be used as a powerful tool for evolution and parameter calculation of international capital flow network.

In the majority of cases, networks are beneficial. However, many times it may also be harmful, such as terrorist networks and disease spreading networks. It has become an urgent challenging problem to disintegrate these harmful networks by various methods such as immunization, block, isolation, disturbance, and attack. The core task of network disintegration is to identify the “critical nodes (edges)”. This survey firstly gives the mathematical description of network disintegration. On this basis, this survey then reviews the status of network disintegration study in the fields of operations research, network science, and computer science based on mathematical programming, the centrality metrics, the heuristic algorithms, evolutionary computation, and machine learning, respectively. Lastly, this survey presents the prospects of network disintegration study from the aspects of the target network, disintegration model, and algorithm.

Opinion reversion is an important phenomenon in network emergencies and hot events. In order to explore the internal mechanism and the evolution law of public opinion reversion, we propose an opinion evolution model based on opinion leaders from the perspective of opinion dynamics. The model is applied to simulate the evolution process of public opinion under the guidance of opinion leaders. We take opinion leaders into account, improve the HK model and use social network analysis method to identify the opinion leaders based on scale-free network structure. To verify the simulation results we select the reversal case on sina twitter. The results show that opinion leaders play a key role in the evolution of opinion, which can guide the public opinion to reverse. The results also indicate that the improved model can simulate the evolution process of network opinion reversion.

This paper introduces the derivation of basic reproduction numbers for several epidemic models. The basic reproduction number plays an important role in describing the dynamic behavior of infectious disease models,which is an important indicator to determine the prevalence of diseases. Therefore, the basic reproductive number is a significant reference for the prevention and control of diseases and the immunization strategy. The basic reproduction numbers can be derived by means of the definition, the monotonicity of the infected individuals at the initial moment, the existence of the positive equilibrium and the local stability of the disease-free equilibrium, the numerical simulation,respectively. This paper introduces many epidemic models especially network model and calculates their basic reproduction numbers. Finally, we analyze the changes in the basic reproduction numbers during different periods.

To improve the ability to predict the evolution trend of public opinion, a public opinion evolution trend prediction model based on an improved wolf pack algorithm and optimized long-short term memory neural network is proposed. Use Halton Sequence to initialization to improve population diversity. Design step factor to perform Gauss-Sine perturbation transformation to improve wolf group exploration and development capabilities. Combine with the spiral in the whale optimization algorithm to improve the siege mechanism to enhance the local search ability of wolves. The bidirectional memory population is used to increase the cooperative ability of the wolf pack. The improved wolf pack algorithm (IWPA) is applied to the hyperparameter prediction of the LSTM neural network. Using keywords such as “COVID-19” and “Food Safety”, the experiment proves that the IWPA-LSTM neural network public opinion evolution prediction model has good accuracy and generality. The model is suitable for the prediction of various public opinion evolution trends.

Complex networks nodes can have multiple attributes, and different attributes or attribute sets will lead to different connections between nodes, thus the network would have different functions.Aiming at the problem that existing complex network models can not construct networks with different functions according to the selected attributes of nodes, a multifunctional complex network model is proposed.The network model is represented only by nodes and their attribute sets. Different network topology and network functions are determined by selecting the attributes of nodes and defining the mapping rules of nodes under the corresponding attributes.By establishing and analyzing a missile defense network, the availability and effectiveness of the multi-functional complex network model are verified

The topological characteristics and resilience analysis of public transportation systems are of great significance in urban management to ensure its safe and sustainable operation. This paper constructs a bus-metro interdependent network model based on the passenger transfer relationship and uses deep learning to identify their network topology attributes. A comprehensive importance indicator of the nodes is established by entropy weight-technique for order preference by similarity to ideal solution (EWM-TOPSIS), and the resilience of the network under different recovery strategies are analyzed. In order to verify the applicability and accuracy of the method, this study takes Wuhan's public transportation network as an example, which has practical guiding significance for the post-disaster recovery and operation management of the urban public transportation system.

Evolutionary games on complex networks is a new interdisciplinary research field at the cross-point of complex networks and evolutionary game. With a complex network and and an evolutionary game dynamics representing the interaction structure among agents and the decision paradigm respectively, evolutionary games on complex networks provides a systematic framework for analyzing and predicting the collective decision-making behaviors of complex interactive populations. This review aims to give a brief survey of evolutionary game dynamics on complex networks from a computational perspective. In detail, we will firstly present a mathematical formulation of the model of evolutionary game dynamics on complex networks, and then analyze the computational complexity of these networked game dynamics, and finally outline some main analytical results about evolutionary game dynamics on complex networks. This computational survey will be a well complement to those simulation results in evolutionary game dynamics on complex networks.

Invulnerability analysis is one of the core contents of power grid security research. Traditional analysis methods cannot effectively analyze the process of failure generation, and have limitations in the research of invulnerability analysis. This paper studies the invulnerability analysis of power networks based on complex network theory, and conducts an empirical analysis using Chongming District of Shanghai as an example. For random attacks and selective attacks on the power network, the changes in the network efficiency and the maximum number of connected subgraphs after the attack are obtained, and the network efficiency change rate is proposed as a parameter to evaluate the invulnerability. According to the simulation results, a segmented protection scheme based on real-time centrality closeness priority attack strategy is proposed to improve the invulnerability of the power network and ensure the safety of the power grid.