Kinetic description and macroscopic limit of swarming dynamics with continuous leader-follower transitions

TL;DR

This paper develops a kinetic and macroscopic model for swarming dynamics with continuous leader-follower transitions, capturing long-range interactions and emergent patterns in multi-agent systems.

Contribution

It introduces a novel kinetic framework incorporating continuous leadership parameters and derives a macroscopic model via hydrodynamic limits, extending previous swarm models.

Findings

The macroscopic model aligns well with particle simulations.

The model reproduces typical swarm patterns.

Long-range interactions are effectively incorporated.

Abstract

In this paper, we derive a kinetic description of swarming particle dynamics in an interacting multi-agent system featuring emerging leaders and followers. Agents are classically characterized by their position and velocity plus a continuous parameter quantifying their degree of leadership. The microscopic processes ruling the change of velocity and degree of leadership are independent, non-conservative and non-local in the physical space, so as to account for long-range interactions. Out of the kinetic description, we obtain then a macroscopic model under a hydrodynamic limit reminiscent of that used to tackle the hydrodynamics of weakly dissipative granular gases, thus relying in particular on a regime of small non-conservative and short-range interactions. Numerical simulations in one- and two-dimensional domains show that the limiting macroscopic model is consistent with the original particle dynamics and furthermore can reproduce classical emerging patterns typically observed in swarms.