Coherent Pattern Prediction in Swarms of Delay-Coupled Agents

TL;DR

This paper analyzes how delay, noise, and coupling influence pattern formation in swarms of self-propelling agents, revealing bifurcation structures and conditions for alignment transitions with hysteresis.

Contribution

It extends previous bifurcation analysis of swarm models by fully unfolding the mean field bifurcation structure and linking it to observed coherent patterns.

Findings

Delay induces pattern bifurcations depending on coupling amplitude.

Large coupling or delay can cause a noise-induced transition to alignment.

Hysteresis occurs in the alignment transition when noise varies over time.

Abstract

We consider a general swarm model of self-propelling agents interacting through a pairwise potential in the presence of noise and communication time delay. Previous work [Phys. Rev. E 77, 035203(R) (2008)] has shown that a communication time delay in the swarm induces a pattern bifurcation that depends on the size of the coupling amplitude. We extend these results by completely unfolding the bifurcation structure of the mean field approximation. Our analysis reveals a direct correspondence between the different dynamical behaviors found in different regions of the coupling-time delay plane with the different classes of simulated coherent swarm patterns. We derive the spatio-temporal scales of the swarm structures, and also demonstrate how the complicated interplay of coupling strength, time delay, noise intensity, and choice of initial conditions can affect the swarm. In particular, our studies show that for sufficiently large values of the coupling strength and/or the time delay, there is a noise intensity threshold that forces a transition of the swarm from a misaligned state into an aligned state. We show that this alignment transition exhibits hysteresis when the noise intensity is taken to be time dependent.