A minimal two-dimensional model explains how a heterogeneous pair of particles self-organizes its trajectory. An active particle, self-propelled along the direction of its instantaneous velocity, is tied by a linear spring to a passive particle that is repelled from it. Integrating the overdamped equations of motion produces three qualitatively distinct collective modes: straight translation, steady circular orbiting, and weaving slalom motion. A linear theoretical analysis reproduces the bifurcation from straight to circular motion as the self-propulsion strength is increased, identifying the mechanistic origin of the pair's dynamical states.
This paper proposes a simple two-dimensional mathematical model for the pairing-induced motion of an active and a passive particle. The two particles are joined by a linear spring; the active particl…