Understanding the cooperation-competition dynamics is a long-standing challenge in studying complex systems.Inspired by the idea of Shannon entropy, we define competition information entropy and propose an entropy evolution model. The analytic results of the model of the relation between competition gain distribution parameters and entropy, as well as the relation between entropy and time are compared with empirical results obtained in 14 real world systems. They are found to be in good agreement with each other.
This paper presents a cellular automaton model for single-lane traffic flow. On the basis of the Nagel-Schreckenberg （NS） model, it further considers the effect of headway-distance between two successive cars on the randomization of the latter one. In numerical simulations, this model shows the following characteristics. （1） With a simple structure, this model succeeds in reproducing the hysteresis effect, which is absent in the NS model. （2） Compared with the slow-tostart models, this model exhibits a local fundamental diagram which is more consistent to empirical observations. （3） This model has much higher efficiency in dissolving congestions compared with the so-called NS model with velocitydependent randomization （VDR model）. （4） This model is more robust when facing traffic obstructions. It can resist much longer shock times and has much shorter relaxation times on the other hand. To summarize, compared with the existing models, this model is quite simple in structure, but has good characteristics.
