Collective dynamics of self-propelled particles with variable speed

TL;DR

This paper introduces a minimal model of self-propelled particles with variable speed influenced by local polarization, revealing new correlation patterns and phase behaviors in collective motion systems.

Contribution

It analytically derives a continuous approximation for variable speed particles and uncovers novel phase-segregation phenomena near the transition to collective motion.

Findings

Variable speed induces inverse power-law correlation between speed and local polarization.

The model predicts a phase-segregated regime with static clusters and high-speed isolated particles.

The continuous approximation accurately describes the system near the transition.

Abstract

Understanding the organization of collective motion in biological systems is an ongoing challenge. In this Paper we consider a minimal model of self-propelled particles with variable speed. Inspired by experimental data from schooling fish, we introduce a power-law dependency of the speed of each particle on the degree of polarization order in its neighborhood. We derive analytically a coarse-grained continuous approximation for this model and find that, while the variable speed rule does not change the details of the ordering transition leading to collective motion, it induces an inverse power-law correlation between the speed or the local polarization order and the local density. Using numerical simulations, we verify the range of validity of this continuous description and explore regimes beyond it. We discover, in disordered states close to the transition, a phase-segregated regime where most particles cluster into almost static groups surrounded by isolated high-speed particles. We argue that the mechanism responsible for this regime could be present in a wide range of collective motion dynamics.