Accelerating consensus of self-driven swarm via adaptive speed

TL;DR

This paper analyzes the convergence time of the Vicsek model and introduces an adaptive speed mechanism to significantly accelerate consensus in self-driven swarms, supported by numerical simulations.

Contribution

It provides a detailed analysis of factors affecting convergence time and proposes a novel variable speed model to enhance convergence speed.

Findings

Convergence time scales as r^2 ln N in noise-free conditions.

Adaptive speed reduces convergence time significantly.

Power law relationship identified for convergence time.

Abstract

In resent years, Vicsek model has attracted more and more attention and been well developed. However, the in-depth analysis on the convergence time are scarce thus far. In this paper, we study some certain factors that mainly govern the convergence time of Vicsek model. By extensively numerical simulations, we find the convergence time scales in a power law with $r^2\ln N$ in the noise-free case, where $r$ and $N$ are horizon radius and the number of particles. Furthermore, to accelerate the convergence, we propose a new model in which the speed of each particle is variable. The convergence time can be remarkably shortened compared with the standard Vicsek model.