Analysis of Autonomous Many-Body Particle Models from Geometric Perspective and Its Applications

Abstract

Autonomous many-body particle systems, such as traffic flow models, pedestrian flow models, and molecular biology models, are very important targets that appear in various fields. Since the behavior of these systems is essentially nonlinear and is rich in variety and flexibility, it is important to grasp the whole picture of the system not only numerically, but also through theoretical analysis. For interacting systems of many-body particles, we have been studying A. the development of analytical methods, B. the investigation and extension of fundamental models.