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Related Experiment Video

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Time-lapse Imaging of Bacterial Swarms and the Collective Stress Response

Time-lapse Imaging of Bacterial Swarms and the Collective Stress Response

Published on: May 23, 2020

Delay-induced instabilities in self-propelling swarms.

Eric Forgoston¹, Ira B Schwartz

¹Nonlinear Dynamical Systems Section, Plasma Physics Division, Code 6792, US Naval Research Laboratory, Washington, DC 20375, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|June 4, 2008

Summary

Adding communication time delay to self-propelled particle models induces a swarm transition, characterized by particle alignment and oscillation, independent of initial swarm state. This transition is linked to a Hopf bifurcation.

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Area of Science:

Complex systems
Statistical physics
Collective behavior

Background:

Self-propelled particle models exhibit transitions between traveling and rotating swarms influenced by noise.
Previous research established noise-induced transitions in swarms of self-propelled particles.

Purpose of the Study:

To investigate the effect of communication time delay on the collective behavior of self-propelled particles.
To identify novel transitions induced by time delays in swarm dynamics.
To analyze the mathematical underpinnings of time-delay-induced transitions.

Main Methods:

Analysis of a general model of self-propelled particles with pairwise attraction, noise, and communication time delay.
Derivation and analysis of mean-field equations in the absence of noise.
Identification of transitions through bifurcation analysis, specifically a Hopf bifurcation.

Main Results:

A time-delay-induced transition occurs, characterized by swarm alignment and oscillation.
This transition is dependent on the coupling amplitude and independent of the initial swarm state (traveling or rotating).
The transition is analytically shown to be associated with a Hopf bifurcation, with good agreement between analytical predictions and numerical computations.

Conclusions:

Communication time delay introduces a new mechanism for controlling swarm behavior, leading to synchronized oscillations and alignment.
Hopf bifurcation analysis provides a robust framework for understanding the emergence of these collective dynamics.
The findings offer insights into the role of delayed interactions in complex adaptive systems.