Research Of Several Kinds Of Dynamic Processes On Complex Networks

Complex network is a new interdisciplinary subject and studied by many researchers. It includes the protein interaction networks, Internet technology networks, interpersonal network, etc. The topology of the network and the dynamic process are the two main research areas. In the complex networks, the nodes represent the individuals and the links represent the relationships between the individuals. Various dynamic models are proposed for the nature and social complex systems. In order to analyse the models, lots of methods from math, physical. are studied.They exactly describe the process of the dynamic. Complex network is practical important not only for our work and daily life, but also for the development of the nature and society.This work is based on some dynamic propagation processes in different network structures. Firstly, we study the dynamic process on the single layer network. Then we introduce the dynamic process on the multi-player network. Finally, the adaptive networks are involved. Three dynamic processes are proposed: the spreading of social contagion, the diffusing of the traffic flow and the transmission of the strategy in game.The main innovations of this paper are as follows:1. Hysteresis loop in social contagionAt present, most of the research are focused on the study without reinfected. There is little research on social contagion with reinfected and threshold spreading model. The analysis results of the reinfected system usually are not very good with the simulation results. But in real lives,there are a large number of reinfected cases. We study the social contagion with the trial state added and traditional social contagion on the community networks. We find that the simulation results agree with the analytical results, and there are hysteresis loops. We provide a theoretical basis for the social contagion with reinfected and threshold spreading model.2. Chain-coupled networksThe traditional network structure only includes the coupling or dependency between the nodes in the network, but ignores the functional characteristics between the nodes. In many cases, a large project or human body system is made up of elements. Although all the elements act differently roles, they are an integral part of the function. If one node is missed, the other nodes could not work properly. The traditional cascade failure model can not be used to discribe the robustness of such networks.We take the bus and subway network system of Beijing as an example to study the robustness of this special chain-coupled network. We solve the problem of robustness assessment of functional networks composed of indispensable functional nodes.3. The dynamics of dilemma gameIn the traditional prisoner's dilemma game, the participant has a single strategy. That can not describe the complex decision-making behavior. So we introduce a third-class participant with multiple strategies. In addition, we study the traditional prisoner's dilemma game on the adaptive network. They are more authentic in describing people's decision-making activities. Both ways can promote the spread of cooperation strategy.This paper is summarized as follows:1. Analyse the dynamic process on single-layer network(1) Based on the social contact and the social cumulative effect, a new social contagion model is proposed to simulate the spreading process of the social behaviors, and the simulating results show that the model is sensitive to the probability of the initial infectors. There is a hysteresis loop for different initial conditions.(2) Based on the traditional prisoner's dilemma game, this paper puts forward the game model with the third-class participant who holds multiple strategies. At the beginning of time steps, the cooperators change their strategy to defection strategy for the high interest of the defectors.However, as there is no benefit between the defectors, the defectors turned to the third class individuals.2. Analyse the dynamic process on multi-layer network(1) Based on the bus and subway systems in Beijing, a new coupled network with chain construction is proposed. It is found that the Beijing subway network is bust to random attacks and target attacks, but the bus network is more robustness to the random attacks than the target attacks.(2) The social contagion with threshold model (SAS) in community network is studied. The optimal community structure which makes the the scope of the transmission is maximum, is found. With the increasing of the links between the communities, the adopters are from only in a community to two communities. If the proportion of coupled links are continu to increase, there is no spreading on either of communities for the reduction of the internal links in the first community.3. Analyse the dynamic process on adaptive networkThe prisoner's dilemma game is analysed on adaptive network. The individual can break links with his weakest neighbor or add new links with his second order neighbors. Through this adaptive adjustment, it is found that the cooperation can be promoted.