Modeling self-organization in pedestrians and animal groups from macroscopic and microscopic viewpoints

TL;DR

This paper introduces a unified mathematical modeling framework using time-evolving measures to analyze self-organization phenomena in pedestrian crowds and animal groups at both macro and micro scales.

Contribution

It presents a novel approach that combines macroscopic and microscopic modeling through time-evolving measures, capturing self-organization from non-local, anisotropic interactions.

Findings

Successful numerical reproduction of self-organized patterns

Unified modeling framework for different scales

Insights into interaction effects on pattern formation

Abstract

This paper is concerned with mathematical modeling of intelligent systems, such as human crowds and animal groups. In particular, the focus is on the emergence of different self-organized patterns from non-locality and anisotropy of the interactions among individuals. A mathematical technique by time-evolving measures is introduced to deal with both macroscopic and microscopic scales within a unified modeling framework. Then self-organization issues are investigated and numerically reproduced at the proper scale, according to the kind of agents under consideration.