基于分数平均场对策的行人群体分数宏微观模型
A Fractional Micro-Macro Model for Crowds of Pedestrians based on Fractional Mean Field Games
摘要：
本文从不同的角度对行人群体的建模进行了研究。在分数维微观模型的基础上，利用质量守恒定律，提出了一个更接近实际的分数维宏观模型。为了刻画行人之间的竞争与合作行为，在宏观尺度上，利用分数平均场对策对行人数量趋于无穷大的情形进行建模，建立了由分数向后和分数向前方程组成的分数动力学模型.最后得到了行人群体的分数微宏模型。仿真结果也分别说明了所提出的分数微观模型和分数宏观模型。
英文摘要：
Modeling of crowds of pedestrians has been considered in this paper from different aspects. Based on fractional microscopic model that may be much more close to reality, a fractional macroscopic model has been proposed using conservation law of mass. Then in order to characterize the competitive and cooperative interactions among pedestrians, fractional mean field games are utilized in the modeling problem when the number of pedestrians goes to infinity and fractional dynamic model composed of fractional backward and fractional forward equations are constructed in macro scale. Fractional micro-macro model for crowds of pedestrians are obtained in the end. Simulation results are also included to illustrate the proposed fractional microscopic model and fractional macroscopic model respectively.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
