Delay Induced Instabilities in Self-Propelling Swarms

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, et al. [Phys. Rev. E {\bf 71}, 051904 (2205)] 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.

4 pages, 5 figures Final revision to appear in PRE Rapid Communications

References in corpus (6)

• Novel type of phase transition in a system of self-driven particles
• Flocks, herds, and schools: A quantitative theory of flocking
• Noise-Induced Transition from Translational to Rotational Motion of Swarms
• Dynamic coordinated control laws in multiple agent models
• A Collective Motion Algorithm for Tracking Time-Dependent Boundaries
• Synchronized dynamics of cortical neurons with time-delay feedback

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