Simple mathematical model for a pairing-induced motion of active and passive particles

TL;DR

This paper introduces a simple mathematical model to describe pairing-induced motion of active and passive particles, capturing various motion patterns and analyzing bifurcations based on self-propulsion strength.

Contribution

The study presents a new minimal model linking active-passive particle interactions with observed motion types and bifurcation behavior.

Findings

Observed straight, circular, and slalom motions in simulations.

Theoretical analysis explains bifurcation between straight and circular motions.

Model captures key dynamics of active-passive particle pairing.

Abstract

We propose a simple mathematical model that describes a pairing-induced motion of active and passive particles in a two-dimensional system, which is motivated by our previous paper [Ishikawa et al., Phys. Rev. E \textbf{106} (2022) 024604]. We assume the following features; the active and passive particles are connected with a linear spring, the active particle is driven in the direction of the current velocity, and the passive particle is repelled from the active particle. A straight motion, a circular motion, and a slalom motion were observed by numerical simulation. Theoretical analysis reproduces the bifurcation between the straight and circular motions depending on the magnitude of self-propulsion.