Flocking dynamics with voter-like interactions

Abstract

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 is reached (polar consensus). We find that increases as t 1/2 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 . At , the mean consensus time scales with the system size N as , and thus the consensus is faster than in the case of all-to-all interactions (large ρ) where . 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.