A Special Case Of The Cooperative And Competitive Network Characteristics And Unified Law Research

This thesis mainly reports the construction, properties and model of world languages network. On the basis of profound in research of a particular system (network of world languages) , we are inclined to investigate the property which plays key role in the process of competition, i.e. the key role of uniqueness in the competition, and research the basic units in different collaboration-competition systems and find the law which the units obey. That is the unified rule which dyads and triads follow. These are the contents we report here as well.In the complex networks, we usually use bipartite graphs to describe a kind of networks. In this kind of networks, there are two sets of nodes, one is called"actors"in which take part events, activities, or organizations (i.e., the participants) and the other is called"acts"(i.e., events, activities, organizations). In the network of world languages, we view languages as"actors"and countries or regions as"acts". In this kind of networks, if we only concern the interaction between actors, a projected single-mode (unipartite) network is often used (projected to the actor set). In this paper, we just pay attention to the relationship between languages, so we project the network into the language set. Meanwhile we use the population of a language to denote the node's weight (that means the nonuniformity of language's population). In this way we get weighted network of world languages. We investigate the topology properties of the world language network after the network is constructed. And we found the distribution of strength has distinct trait.That is the world languages can be divided into two kinds clearly from the figure of the language's strength distribution(i.e. the duality of world languages). We call them active languages and inactive languages. That did not find and mention in traditional language research. In order to understand the duality of world languages better, we propose a minimal model to explain the may mechanism dynamics of world languages'evolution. The model gets ideal outcome in the most simple condition without considering the factor of language population. Then we consider the influence of language population and fine the model further. The analytic strength distribution of world language network fits the empirical investigation well. Meanwhile the model can get other statistic properties analytically and fits the empirical investigation as well. That show we catch the key factor of world languages'evolution, and in a certain degree show our model can stand up.In the research of complex networks, collaboration networks and collaboration-competition networks attract a lot of attention. Many experts and scholars propose a lot of brilliant ideas, but these ideas are just qualitative description and do not present quantitative one. In our study, we present a quantitative expression of a well accepted idea about collaboration and competition: uniqueness is important in competition. In order to quantify this expression, we suggest two new statistical quantity called"competition ability"and"uniqueness". We analyze the relationship of the two quantity and find they are equal in ordinary case. This means that uniqueness completely drives the competition. In order to check our outcome, we apply it to regional university system and find the empirical investigation in accord with our analytic outcome. That shows the two quantity we proposed is valuable and can give good advice to our real life.In the end of the thesis, we report the unified law the dyads and triads obey in cooperation. This research aims at different systems. Thought the systems cross a lot of subjects, all the act degree distribution of their dyads and triads obey the same law, i.e. the"shifted power law"which is advocated by our group. This work extend our work before, therefore it is our key report as well.