Flocking dynamics with voter-like interactions

• Published in: Journal of statistical mechanics Vol. 2018; no. 3; pp. 33403 - 33419
• Main Authors: Baglietto, Gabriel, Vazquez, Federico
• Format: Journal Article
• Language: English
• Published: IOP Publishing and SISSA 12.03.2018
• ISSN: 1742-5468; 1742-5468
• DOI: 10.1088/1742-5468/aaac3e

We study the collective motion of a large set of self-propelled particles subject to voter-like interactions. Each particle moves on a 2D space at a constant speed in a direction that is randomly assigned initially. Then, at every step of the dynamics, each particle adopts the direction of motion of a randomly chosen neighboring particle. We investigate the time evolution of the global alignment of particles measured by the order parameter , until complete order φ=1.0 is reached (polar consensus). We find that increases as t1/2 for short times and approaches 1.0 exponentially fast for longer times. Also, the mean time to consensus τ varies non-monotonically with the density of particles ρ, reaching a minimum at some intermediate density ρmin. At ρmin, the mean consensus time scales with the system size N as τmin∼N0.765, and thus the consensus is faster than in the case of all-to-all interactions (large ρ) where τ=2N. We show that the fast consensus, also observed at intermediate and high densities, is a consequence of the segregation of the system into clusters of equally-oriented particles which breaks the balance of transitions between directional states in well mixed systems.