Macroscopic models of collective motion and self-organization

TL;DR

This paper reviews the development of macroscopic models for collective motion, focusing on the derivation of the Self-Organized Hydrodynamics (SOH) model from particle interactions, and discusses its properties and extensions.

Contribution

It provides a comprehensive review of the derivation, properties, and potential extensions of the SOH model for collective motion.

Findings

Existence results for the SOH model

Properties of the SOH model

Potential extensions to other collective behaviors

Abstract

In this paper, we review recent developments on the derivation and properties of macroscopic models of collective motion and self-organization. The starting point is a model of self-propelled particles interacting with its neighbors through alignment. We successively derive a mean-field model and its hydrodynamic limit. The resulting macroscopic model is the Self-Organized Hydrodynamics (SOH). We review the available existence results and known properties of the SOH model and discuss it in view of its possible extensions to other kinds of collective motion.