Xiu-Lian Xu

An evolution model of complex systems with simultaneous cooperation and competition

Systems with simultaneous cooperation and competition among the elements are ubiquitous. In spite of their practical importance, knowledge on the evolution mechanism of this class of complex system is still very limited. In this work, by conducting extensive empirical survey to a large number of cooperation–competition systems which cover wide categories and contain the information of network topology, cooperation–competition gain, and the evolution time, we try to get some insights into the universal mechanism of their evolutions. Empirical investigations show that the distributions of cooperation–competition gain interpolates between the power law function and the exponential function. Particularly, we found that the cooperation–competition systems with longer evolution durations tend to have more heterogeneous distributions of cooperation–competition gain. Such an empirical observation can be well explained by an analytic model in which the evolution of the systems are mainly controlled by the Matthew effect, and the marginal heterogeneity of the initial distribution is amplified by the Matthew effect with similar speed in spite of the diversity of the investigated systems.

Recognition of Important Subgraphs in Collaboration Networks

We propose a method for recognition of most important subgraphs in collaboration networks. The networks can be described by bipartite graphs, where basic elements, named actors, are taking part in events, organizations or activities, named acts. It is suggested that the subgraphs can be described by so-called k-cliques, which are defined as complete subgraphs of two or more vertices. The k-clique act degree is defined as the number of acts, in which a k-clique takes part. The k-clique act degree distribution in collaboration networks is investigated via a simplified model. The analytic treatment on the model leads to a conclusion that the distribution obeys a so-called shifted power law P(q) ∝ (q + α) − γ where α and γ are constants. This is a very uneven distribution. Numerical simulations have been performed, which show that the model analytic conclusion remains qualitatively correct when the model is revised to approach the real world evolution situation. Some empirical investigation results are presented, which support the model conclusion. We consider the cliques, which take part in the largest number of acts, as the most important ones. With this understanding we are able to distinguish some most important cliques in the real world networks.

A Collaboration Network Model with Multiple Evolving Factors

To describe the empirical data of collaboration networks, several evolving mechanisms have been proposed, which usually introduce different dynamics factors controlling the network growth. These models can reasonably reproduce the empirical degree distributions for a number of well-studied real-world collaboration networks. On the basis of the previous studies, in this work we propose a collaboration network model in which the network growth is simultaneously controlled by three factors, including partial preferential attachment, partial random attachment and network growth speed. By using a rate equation method, we obtain an analytical formula for the act degree distribution. We discuss the dependence of the act degree distribution on these different dynamics factors. By fitting to the empirical data of two typical collaboration networks, we can extract the respective contributions of these dynamics factors to the evolution of each networks.