Towards a mathematical theory of behavioral swarms

TL;DR

This paper develops a unified mathematical framework for behavioral swarms, integrating social behavior dynamics with particle mechanics, and demonstrates its applicability to existing models like Cucker-Smale.

Contribution

It introduces the concept of behavioral swarms and provides a comprehensive mathematical theory that encompasses and extends existing swarm models.

Findings

Several Cucker-Smale type models are unified under the new framework.

The theory offers a foundation for future research beyond current models.

Applications demonstrate the versatility of the proposed approach.

Abstract

This paper presents a unified mathematical theory of swarms where the dynamics of social behaviors interacts with the mechanical dynamics of self-propelled particles. The term behavioral swarms is introduced to characterize the specific object of the theory which is subsequently followed by applications. As concrete examples for our unified approach, we show that several Cucker-Smale type models with internal variables fall down to our framework. Subsequently the modeling goes beyond the Cucker-Smale approach and looks ahead to research perspectives.