Generalized Cooperative Network And Its Related Studies

The dynamics principles, which describe the actors'behaviors in complex self-adaptive systems, should include some characters similar to what are shown by the living systems, such as forecasting, choice, learning, and evolution. Each actor and his behavior are different. Also, a system consisting of actors is not a simple combination of them. It cannot be treated by reduction theory, and cannot be described by the conventional mathematics, which serve for determinism and reductionism. We must develop some new methods and tools to describe self-adaptive systems. The latest development in the complex network gives us a possible way for searching the possibility.The complex network can describe variety different practical systems. We have carried out empirical studies on quite some practical systems; wish to classify the systems based on the results and find out the common statistical properties of every kind of them. The next step could be setting up suitable models so that we could understand their common dynamical characteristics and mechanism. In this way we can reach, step by step, to a more universal understanding on complex systems. Among the very wide scope of complex network studying, our interests are concentrated on the so-called"generalized collaboration networks". In such networks the nodes (actors) are participating a lot of collaborative acts. In the study we shall only consider actor's cooperation, and ignore the competition, confrontation or other type of relations between them. We propose define actor's cooperation in the acts as edges. In this way, one act can be described by a complete graph composed by the actors where every pair of them are connected with edges. Such a network may not be a social network, it can belong to many other kinds of networks too, but because the topological structure has common characteristics, their statistics properties have common characteristics. Among the practical networks we empirically studied, we found that the Chinese tourist line network, the urban public traffic network, the traditional Chinese medicine prescription network, and Huai-Yang recipe network can be described by the generalized collaboration networks. After the analysis on the empirical data, we have obtained some common statistical properties: First of all, the act is a leading factor in this kind of networks. The act degree distribution (the distribution of the number of the acts, in which the actors are participating) should be, very possibly, the most important property in such kinds of networks. It, in a great extent, determines the node strength degree and degree distribution. Secondly, the assortativity of the actors shows a monotonic change with the change of such distribution law. We propose a simplified model based on these ideas so as to show the common dynamical mechanisms of the two common properties. The analytic and numerical investigation results of the model show very good agreement with the empirical results. Finally, according to the common topological characteristics of the so-called generalized collaboration networks, we propose a quantitative definition and corresponding division method for community and hierarchy. A new network statistical property, the degree of interweavement, has been proposed by this consideration that may have practical importance.Since urban public traffic systems are practically important, they have been extensively and intensively studied. We have studied urban public traffic networks from the viewpoint of complex networks and game theory. From that, we have suggested three manipulator game models of urban public traffic networks continuously. We try to construct a simplest model with the idea that hits the nail on the head. In this paper, we mainly present the last model of the three. We suggest a very simplified viewpoint in which the evolution of urban public traffic network can be considered as a game process between the two network manipulators, and the equilibrium solution of the game determines the last evolution tendency of the network. We have performed analytical discussion on some extreme and the equilibrium situations and numerical discussion on the general evolution, the obtained statistical properties are in a good agreement with the empirical ones obtained by the investigations on the urban public traffic systems in Beijing, Shanghai, Nanjing and Hangzhou. This shows that the model grasps the most fundamental characteristic of the system. The idea, very possibly, can be extended and used in many other systems.Generalized collaboration networks ignore the factor of competition. If competition joins in network, what characteristic may appear? As for it, we introduce three systems which take competition into account. The research is rough. However, we expect as a beginning, the work could inspire people to research the collaboration and competition network deeply.