Two improved Vicsek models with different coupling strengths between particles

Abstract

In the original Vicsek model, each particle needs to know its total neighbors’ direction and does not distinguish the coupling strength between them. However, it is very slow to achieve consensus when the density of particles is too high. In this paper, in order to differentiate the coupling strength according to the Euclidean distance between particles, we proposed a new rule and introduced two improved Vicsek models based on this rule. The improved model I puts the exponential symbolic coupling function into the original Vicsek model, and the improved model II puts the exponential Sigmoid coupling function into the original Vicsek model. Simulations show these two kinds of improved Vicsek models all have less convergence steps than the original Vicsek model under different system parameters. Furthermore, when the exponent increases from 1, the convergence steps could be further reduced, then gradually stay unchanged.