Noise and synchronization of a single active colloid

A two-state oscillator in a viscous liquid is composed of a micron-scale particle whose intrinsic dynamics is defined by linear potentials that undergo configuration-coupled transitions and is externally driven by a piecewise constant periodic force of varying amplitude and frequency. This elementary example of "active matter" has the minimal elements that allow us to study synchronization in the presence of thermal fluctuations. Experiments reveal the presence of synchronized states (and Arnol'd tongues), which we explain using analytical and numerical calculations. The system maintains synchronization by adjusting the phase between the bead and the clock. We discuss the relevance of this model to synchronization in real-world systems, including the role of thermal noise.