Delay-induced instabilities in self-propelling swarms

Eric Forgoston, Ira B. Schwartz

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

We consider a general model of self-propelling particles interacting through a pairwise attractive force in the presence of noise and communication time delay. Previous work by Erdmann [Phys. Rev. E 71, 051904 (2005)] has shown that a large enough noise intensity will cause a translating swarm of individuals to transition to a rotating swarm with a stationary center of mass. We show that with the addition of a time delay, the model possesses a transition that depends on the size of the coupling amplitude. This transition is independent of the initial swarm state (traveling or rotating) and is characterized by the alignment of all of the individuals along with a swarm oscillation. By considering the mean field equations without noise, we show that the time-delay-induced transition is associated with a Hopf bifurcation. The analytical result yields good agreement with numerical computations of the value of the coupling parameter at the Hopf point.

Original languageEnglish
Article number035203
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume77
Issue number3
DOIs
StatePublished - 19 Mar 2008

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Swarm
Time Delay
time lag
Rotating
Mean Field Equation
Communication Delay
translating
noise intensity
Barycentre
Hopf Bifurcation
Numerical Computation
center of mass
Pairwise
Alignment
communication
alignment
Oscillation
oscillations
causes
Model

Cite this

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Delay-induced instabilities in self-propelling swarms. / Forgoston, Eric; Schwartz, Ira B.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 77, No. 3, 035203, 19.03.2008.

Research output: Contribution to journalArticle

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