Flocking dynamics with voter-like interactions - Baglietto, Gabriel; Vazquez, Federico (arXiv.org, 2019)
We study the collective motion of a large set of self-propelled particles subject to voter-like interactions. Each particle moves on a two-dimensional 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 \(φ\), until complete order \(φ=1.0\) is reached (polar consensus). We find that \(φ\) increases as \(t^{1/2}\) for short times and approaches exponentially fast to \(1.0\) for long times. Also, the mean time to consensus \(τ\) varies non-monotonically with the density of particles \(ρ\), reaching a minimum at some intermediate density \(ρ_{\tiny min}\). At \(ρ_{\tiny min}\), the mean consensus time scales with the system size \(N\) as \(τ_{\tiny min} \sim N^{0.765}\), 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.