  Synchronisation and stability under periodic oscillatory driving are
well-understood, but little is known about the effects of aperiodic driving,
despite its abundance in nature. Here, we consider oscillators subject to
driving with slowly varying frequency, and investigate both short-term and
long-term stability properties. For a phase oscillator, we find that,
counter-intuitively, such variation is guaranteed to enlarge the Arnold tongue
in parameter space. Using analytical and numerical methods that provide
information on time-variable dynamical properties, we find that the growth of
the Arnold tongue is specifically due to the growth of a region of intermittent
synchronisation where trajectories alternate between short-term stability and
short-term neutral stability, giving rise to stability on average. We also
present examples of higher-dimensional nonlinear oscillators where a similar
stabilisation phenomenon is numerically observed. Our findings help support the
case that in general, deterministic non-autonomous perturbation is a very good
candidate for stabilising complex dynamics.
