Abstract
In the original Vicsek model, the motion direction of a particle is updated according to its all neighbors’ mean direction. However, the convergence speed of the system is usually low due to the too many interacting particles, which is especially true when the particle densities are high. Therefore, a new rule is proposed to make the motion direction of all particles reach consensus more quickly. The Euclidean distances between its neighbors and the particle are arranged from far to near, and we only take the average direction of the farthest part neighbors as the motion direction of the particle at the next moment, which replace the original Vicsek model. The simulation results demonstrate that the improved Vicsek model has faster convergence speed than the original Vicsek model under different particle number and different system parameters. Furthermore, the convergence speed will reach the fastest with an appropriate number of neighbors according to the new rule, and the improved model is much easier to obtain consensus even for the noise disturbance.
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