  Van der Pol oscillators are prototypical self-sustaining oscillators which
have been used to model nonlinear processes in biological and other classical
processes. In this work, we investigate how quantum fluctuations affect
phase-locking in one or many van der Pol oscillators. We find that
phase-locking is much more robust in the quantum model than in the equivalent
classical model. Trapped-ion experiments are ideally suited to simulate van der
Pol oscillators in the quantum regime via sideband heating and cooling of
motional modes. We provide realistic experimental parameters for
${}^{171}\text{Yb}^+$ achievable with current technology.
