Noise, Bifurcations, and Modeling of Interacting Particle Systems

TL;DR

This paper analyzes how noise and communication delays influence pattern formation in large systems of interacting self-propelled particles, revealing bifurcations between translating and rotating states.

Contribution

It introduces a mean field model to describe bifurcation patterns caused by noise, delay, and coupling in particle systems, advancing understanding of collective dynamics.

Findings

High noise induces a transition from translation to rotation.

Communication delay causes bifurcations dependent on coupling strength.

Patterns include translation, stationary rotation, and rotating swarm states.

Abstract

We consider the stochastic patterns of a system of communicating, or coupled, self-propelled particles in the presence of noise and communication time delay. For sufficiently large environmental noise, there exists a transition between a translating state and a rotating state with stationary center of mass. Time delayed communication creates a bifurcation pattern dependent on the coupling amplitude between particles. Using a mean field model in the large number limit, we show how the complete bifurcation unfolds in the presence of communication delay and coupling amplitude. Relative to the center of mass, the patterns can then be described as transitions between translation, rotation about a stationary point, or a rotating swarm, where the center of mass undergoes a Hopf bifurcation from steady state to a limit cycle. Examples of some of the stochastic patterns will be given for large numbers of particles.