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.