Kuramoto model with run-and-tumble dynamics

TL;DR

This paper extends the Kuramoto model by incorporating run-and-tumble dynamics, allowing particles' angular velocities to change randomly, and studies phase transitions in this self-propelled particle system.

Contribution

It introduces a novel extension of the Kuramoto model with stochastic angular velocity changes and analyzes phase transition behavior in this new context.

Findings

The extended model exhibits a phase transition similar to the original Kuramoto model.

The distribution g(w) influences the nature of the phase transition.

Self-propelled particles with run-and-tumble dynamics can be effectively modeled within this framework.

Abstract

This work considers an extension of the Kuramoto model with run-and-tumble dynamics -- a type of self-propelled motion. The difference between the extended and the original model is that in the extended version angular velocity of individual particles is no longer fixed but can change sporadically with a new velocity drawn from a distribution g(w). Because the Kuramoto model undergoes a phase transition, it offers a simple case study for investigating phase transition for a system with self-propelled particles.