Research on Swarm Convergence Performance of Saturated Vicsek Model

In this paper, we proposed a saturated self-propelled particle system, where the weight between two particles could be saturated if the Euclidean distance between particles is smaller than a certain value or bigger than a certain value. In order to represent the weight of each particle, we introduced the saturated piecewise function into original Vicsek model, the bounds of the function are fixed value. Furthermore, due to different upper limit value could result in different convergence speed, we introduce a exponent into upper limit of saturation and investigate the convergence of the system when the upper limit increases exponentially. The simulation results demonstrate that the saturated model has faster convergence speed than original Vicsek model under different particle number and different system parameters and the convergence speed can be further improved as the exponent increases, the system is much easier to obtain consensus even for the noise disturbance.