Investigation Of Some Dynamic Topics On Complex Networks

Many natural and artificial systems in the real world can be described by complex network. Since most of the network topological structures were found to show a small-world and a scale-free feature, complex networks have attracted growing interest among the physics community. A major goal of investigation is to unveil how the topological structures of networks influences the dynamical processes on them.For modern society, it is of great importance to study the dynamical processes of the transportation of information or matter on networks, which is one of the basic functions of networks. We constructed a simple model to study the congestion dynamic triggered by multiple particles walking along the shortest path on complex networks which composed of nodes that have a finite capacity. It is found that a transition from free-flow phase to congestion phase occurs at a critical particle density, which varies for complex networks with different topological structures. The dynamic pictures of congestion for networks with different topological structures show that congestion on scale-free networks is a percolation process of many small congestion clusters, while the dynamic of congestion transition on other three homogenous networks is mainly a process of nucleation in analogy to crystal growth.To explain the emergence of cooperation by natural selection has been a fundamental topic of evolutionary biology since Darwin. Evolutionary game theory provides a uniform frame to study the evolution of cooperation. We investigate the evolution of strategies in the iterated prisoner's Dilemma game and hawk-dove game on complex networks on the basis of genetic algorithm, and the assumption that individuals on complex networks only play games with their neighbors. These individuals have historical memory to update their strategies based on their genotype and the knowledge of past game record. It is found that the individuals can naturally develop some self-organization mechanics of cooperation by genome reproduction, recombination, mutation and selection, which can not only result in the emergence of cooperation, but also strengthen and sustain the persistent cooperation. At the same time, such mechanics punishes and revenges defective individuals, leading to a high cooperation frequency on complex networks.