Modeling self-organized systems interacting with few individuals: from microscopic to macroscopic dynamics

TL;DR

This paper develops a multiscale modeling framework for self-organized systems like flocks and herds interacting with external agents, deriving microscopic, kinetic, and macroscopic descriptions.

Contribution

It introduces a systematic derivation of macroscopic models from microscopic dynamics for systems influenced by external point sources.

Findings

Derived kinetic model via mean-field limit

Obtained macroscopic equations through hydrodynamic limit

Applicable to biological systems with external influences

Abstract

In nature self-organized systems as flock of birds, school of fishes or herd of sheeps have to deal with the presence of external agents such as predators or leaders which modify their internal dynamic. Such situations take into account a large number of individuals with their own social behavior which interact with a few number of other individuals acting as external point source forces. Starting from the microscopic description we derive the kinetic model through a mean-field limit and finally the macroscopic system through a suitable hydrodynamic limit.