Critical transition for colliding swarms

TL;DR

This paper develops a mean-field analytical approach to predict the conditions under which colliding swarms form a stable milling state, validated by multi-agent simulations, advancing understanding of swarm-on-swarm interactions.

Contribution

It introduces a mean-field model to predict the critical interaction strength for stable milling in colliding swarms, extending prior numerical studies.

Findings

Critical coupling predicts milling formation in colliding swarms.

Analytical predictions match multi-agent simulation results.

Identifies a saddle-node bifurcation as the transition point.

Abstract

Swarming patterns that emerge from the interaction of many mobile agents are a subject of great interest in fields ranging from biology to physics and robotics. In some application areas, multiple swarms effectively interact and collide, producing complex spatiotemporal patterns. Recent studies have begun to address swarm-on-swarm dynamics, and in particular the scattering of two large, colliding swarms with nonlinear interactions. To build on early numerical insights, we develop a mean-field approach that can be used to predict the parameters under which colliding swarms are expected to form a milling state. Our analytical method relies on the assumption that, upon collision, two swarms oscillate near a limit-cycle, where each swarm rotates around the other while maintaining an approximately constant and uniform density. Using this approach we are able to predict the critical swarm-on-swarm interaction coupling, below which two colliding swarms merely scatter, for near head-on collisions as a function of control parameters. We show that the critical coupling corresponds to a saddle-node bifurcation of a stable limit cycle in the uniform, constant density approximation. Our results are tested and found to agree with large multi-agent simulations.