EMERGENT COLLECTIVE BEHAVIOR: PROBING THE DENSITY DEPENDENCE WITH THE VICSEK MODEL

Abstract

The Vicsek model provides as a primary outline for studying the emergence of collective motion or “flocking” from simple limited interaction rules among self – propelled particles. This work examines the particular effect of particle density on the collective behaviour and commanding within such an organization. Simulations were carried out using FORTRAN program in a Linux atmosphere, with parameters including particle speed, noise and interaction radius held constant whereas carefully varying the number of particles (N) from 10 to 2000 within a fixed spatial box. The normalized average velocity (va) was used for quantifying the degree of collective motion. The results reveal apparent and non-monotonic reliance behaviour on particle density. Particles move independently with minimal consistency at very low densities. By increasing density, transitions takes place where particles begin to form coherently moving clusters. Although, at intermediary densities, group formation can lead to a decrease in universal order if groups move in dissimilar directions. At extremely high densities, a high degree of global alignment is constantly covered, with the system possessing strong polar order (va ≈ 0.999). The present work concludes that while enhancing density usually promotes collective motion, the relation is complicated, with optimal global coordination emerging at sufficiently high densities where local interactions percolate throughout the complete system.