The evaluation of emergent behaviors on an improved Vicsek model

Emergence is a new feature of complex system, which is not attributed to any individual but as a global outcome of individual coordination. While there yet isn´t a clear mathematical definition about emergence, the emergence evaluation metrics, as a new method for analyzing emergent behaviors, can give the process of emerging more intuitive observation and interpretation. However, due to lacking of theoretical proof, the universality of those metrics is still questionable. In response to the question whether the emergence evaluation metrics is universal, we propose a new Vicsek model (WAR-Vicsek), which is based on weighted attractive-repulsive. Firstly some emergent behaviors are discovered in this model for the first time. Then, its emergent behaviors are analyzed by using the evaluation metrics such as the neighborhood individual distributes index and the degree of average individual interaction. Simulation experiment results demonstrate that the change process of the evaluation metrics curves can reflect the current phase of emergent behavior effectively. And it is also proved that these evaluation metrics are universal in this model.