Dynamics Research On Complex Networks And Application Of Evolutionary Games

Recently, the study of complex networks has permeated form math and physics to biology, informatics, engineering, and sociology and so on. To explore the qualitative characters and the quantitative rules of complex networks and the effect of topology emergence has become one important lesson of the study of complex networks. Therefore, the study of complex networks is very profound. In the paper, we applied theories of chaos dynamics, statistical physics, matrix analysis, and used computer calculating method to study synchronization, attack and games on complex networks.In this paper, we discussed the research background of the complex networks theory and its fundamental theory, such as the mean shortest path-length, the networks'topological parameters, etc. We also discussed some basic networks topologies, which have been widely studied and also serve as the base of our research work. Then we research three objects about complex networks:synchronization, attack and games. We have made the following three contributions in our research work:First, we realized the method to improve synchronization of the complex networks by adding weight to edges.Second, we proposed a novel method for estimating the weight distribution of a network and taking effective attacks with Gauss edge weights using a time series collected from controlled measurements of the stable dynamics of the network. We found that this scheme can explore the topological structures of the whole networks in completed ignorance of the network topology and dynamics. Finally, the method here is rather robust against noise and can be applicable to a broad coupling strength region.Finally, we further study the competition among loner, cooperative and defective strategies by considering an evolutionary prisoner's dilemma game with some troublemakers in the random network by means of Monte Carlo simulations. It can be observed that the frequency of cooperators decreases with increasing of loners' and defectors' payoffs. In practice, it also prevents cooperative strategies and defective strategies from vanishing for large e values.