Research Of Naming Games In Complex Networks

Naming games is recently studied by statistical physicists. As a simple model to explain the evolution of language in history, it can reveal that without the control or interruption by anyone, people in one large group would gradually use the same words of this language after many years. Also, naming game can present the process of language, such as the S-shape in the development of word numbers for one object. From Semiotic dynamics, we find naming game model is related with the size of network and the time of evolution. We introduce the effect of memory to this model and find some parameters in modified model can behave better than before. The paper is organized as follows:In chapter 1, we introduce some statistical models in sociology. As the combinations of sociology and physics, those models are build by the conceptions of mathematics or physics. From those models, which are connected with economics, opinion and immunity, we notice that many phenomenon can reflect characteristics by simulation and analysis, especially the time and topological characteristics of degree distribution. We would pay attention to Sznajd model, voter model, Glauber Ising model. Then complex networks would be explained because all the models are just mechanisms that should be applied in networks. We will introduce small-world networks and scale-free networks, which have been proved in simulations of reality with lots mechanisms. In chapter 2, we begin to study the background of naming games. First, we notice that scientists have already thought of the causes for evolution in language and have got some fruitful results. It is obvious that with the boom in computer science, the simulation of language in large group came true. At the same time, physicists simplify this simulation with previous models. Then the consensus in naming one object is revealed. Furthermore, some self-organization properties in naming games are studied. Others start to investigate the influence of networks and the length of memory.In chapter 3, we propose memory-based naming games, which would not delete all the memory in the evolution. Considering previous models, we modify naming games to an two-variables models and find that it is different between modified naming games and before. With the method of fitting, we find this modified model is sensitive to the initial values and thresholds. In order to improve our model, we adopt forgetting curve of Ebbinghaus. Some of the results also behave as scaling laws.Conclusions and outlook are given in Chapter 4.