Study Of Some Dynamics On The Complex Networks

The study of complex network is new and interdisciplinary science, which refers to fields of physics, maths, biology and social science. In the past decade, the study of complex network has received much attention from many scientists in various fields and developed rapidly.There are various complex networks in nature and human society, such as metabolism networks, genetic regulatory networks, neural networks, railway networks, Internet, power grids, social relation networks and so on. After extensive studies, people find that many real networks have some similar property, such as small-world effect and power-law distribution. To reflect the structures of real networks, scientists have proposed some typical comlex network models, such as Watts-Strogatz small-world networks and Barabási-Albert scale-free networks. These simple models can recover the property of real networks. Many reasearches has been performed on these models.After the understanding of the property of real networks, people pay more attention to various dynamics happening on networks, such as evolutionary games, opinion dynamics, the evolution of language, information flow, epidemic spreading, cascading failure, synchronization and so on. By investigating various dynamics on networks, people can deeply understand many phenomena existing in nature and human society, such as the emergence and maintenance of cooperative behavior, the jam of traffic and imformation, the spread of epidemic and the accident of power cut. The study of various dynamics on networks can help people solve many problems, such as the traffic jam and epidemic spreading.There are much dynamics on networks. In this dissertation, we foucs on some important dynamics, including evolutionary games, the information flow and opinion dynamics.The main content of this dissertation are summarized as follows:We study the evolutionary games on complex networks, including the prisoner's dilemma game and the public goods game. We study how the clustering structure, social diversity and aspiration-induced migration affect the cooperative behavior. We find that the higher clustering coefficient enhances the cooperation in spatial public goods game. Due to the existence of social diversity, the influence of different individuals is different. We define the influence of an individual is the power of its degree, where the power exponentαis an adjustable parameter. During the evolutionary process, every individual chooses one of its neighbors as a reference with a probability proportional to the influence of the neighbor. It is found that for the fixed value of the temptation to defect, there exists an optimal value ofα, leading to the highest level of cooperation. We propose an aspiration-induced migration in which individuals will migrate to new sites provided that their payoffs are below some aspiration level. It is found that moderate aspiration level can best favor cooperative behavior.We study the information flow on the complex networks. When the total node's packet-delivering capacity is fixed, we design a best allocation of packet-delivering capacity on different nodes, which maximizes the network capacity. We first study the information transportation on mobile networks. It is found that the network capacity can be enlarged when the moving speed and the communication range increases. Our study would be useful for the design of Wireless Mobile Ac Hoc Network.We study the opinion dynamics on complex networks. We study effect of the heterogenous influence of individuals on voter model. The opinion of an individual with larger influence is more likely to be follwed by other individuals. It is found that the consensus can be fastest reached when the large-degree individuals have suitably large influence. Moreover, we study the role of conformist mentality in the opinion dynamics. It is found that the system can fastest reach consensus when individuals suitably follow the majority opinion among their neighbors.