Transition to Synchrony in a Three-Dimensional Swarming Model with Helical Trajectories

TL;DR

This paper studies how a 3D swarming model with helical trajectories transitions from incoherence to collective motion, showing how noise influences the nature of this transition and the resulting collective behaviors.

Contribution

It introduces a noise-regularized version of a 3D swarming model with helical trajectories, revealing continuous transition behaviors not seen in the noiseless case.

Findings

Noise converts discontinuous transitions into continuous ones.

The model exhibits directed collective motion or center-of-mass rotations.

Helical trajectories influence the nature of the collective transition.

Abstract

We investigate the transition from incoherence to global collective motion in a three-dimensional swarming model of agents with helical trajectories, subject to noise and global coupling. Without noise this model was recently proposed as a generalization of the Kuramoto model and it was found that alignment of the velocities occurs discontinuously for arbitrarily small attractive coupling. Adding noise to the system resolves this singular limit and leads to a continuous transition, either to a directed collective motion or to center-of-mass rotations.