How environment affects active particle swarms: a case study

TL;DR

This paper explores how environmental obstacles influence active particle swarms, revealing key forces driving pattern formation and introducing a novel method to compare discrete and continuum models for better understanding collective behaviors.

Contribution

It provides a detailed analysis of pattern formation mechanisms in active swarms with environmental feedback and introduces a new methodology for comparing discrete and continuum models.

Findings

Agent-agent, agent-obstacle, and spring stiffness are key to pattern emergence.

Alignment forces are less influential in pattern formation.

Discrete and continuum models show good agreement under certain conditions.

Abstract

We investigate the collective motion of self-propelled agents in an environment filled with obstacles that are tethered to fixed positions via springs. The active particles are able to modify the environment by moving the obstacles through repulsion forces. This creates feedback interactions between the particles and the obstacles from which a breadth of patterns emerges (trails, band, clusters, honey-comb structures,...). We will focus on a discrete model first introduced in [Aceves2020] and derived into a continuum PDE model. As a first major novelty, we perform an in-depth investigation of pattern formation of the discrete and continuum models in 2D: we provide phase-diagrams and determine the key mechanisms for bifurcations to happen using linear stability analysis. As a result, we discover that the agent-agent repulsion, the agent-obstacle repulsion and the obstacle's spring stiffness are the key forces in the appearance of patterns, while alignment forces between the particles play a secondary role. The second major novelty lies in the development of an innovative methodology to compare discrete and continuum models that we apply here to perform an in-depth analysis of the agreement between the discrete and continuum models.