Signal propagation and linear response in the delay Vicsek model

Abstract

Retardation between sensation and action is an inherent biological trait. Here we study its effect in the Vicsek model, which is a paradigmatic swarm model. We find that: (i) a discrete time delay in the orientational interactions diminishes the ability of strongly aligned swarms to follow a leader and, in return, increases their stability against random orientation fluctuations; (ii) both longer delays and higher speeds favor ballistic over diffusive spreading of information (orientation) through the swarm; (iii) for short delays, the mean change in the total orientation (the order parameter) scales linearly in a small orientational bias of the leaders and inversely in the delay time, while its variance first increases and then saturates with increasing delays; (iv) the linear response breaks down when orientation conservation is broken.

13 pages, 9 figues

References in corpus (11)

• Novel type of phase transition in a system of self-driven particles
• Interaction Ruling Animal Collective Behaviour Depends on Topological rather than Metric Distance: Evidence from a Field Study
• Motility-Induced Phase Separation
• Hierarchical group dynamics in pigeon flocks
• Collective motion of self-propelled particles interacting without cohesion
• Fluctuations and response of nonequilibrium states
• Pattern formation in self-propelled particles with density-dependent motility
• Inertial effects of self-propelled particles: from active Brownian to active Langevin motion
• Initiation and spread of escape waves within animal groups
• Delay Induced Instabilities in Self-Propelling Swarms
• Silent Flocks

Cited by in corpus (2)

• Scale-free chaos in the 2D harmonically confined Vicsek model
• Power laws of natural swarms are fingerprints of an extended critical region