  Nonautonomous driving of an oscillator has been shown to enlarge the Arnold
tongue in parameter space, but little is known about the analogous effect for a
network of oscillators. To test the hypothesis that deterministic nonautonomous
perturbation is a good candidate for stabilising complex dynamics, we consider
a network of identical phase oscillators driven by an oscillator with a slowly
time-varying frequency. We investigate both the short- and long-term stability
of the synchronous solutions of this nonautonomous system. For attractive
couplings we show that the region of stability grows as the amplitude of the
frequency modulation is increased, through the birth of an intermittent
synchronisation regime. For repulsive couplings, we propose a control strategy
to stabilise the dynamics by altering very slightly the network topology. We
also show how, without changing the topology, time-variability in the driving
frequency can itself stabilise the dynamics. As a by-product of the analysis,
we observe chimera-like states. We conclude that time-variability-induced
stability phenomena are also present in networks, reinforcing the idea that
this is quite realistic scenario for living systems to use in maintaining their
functioning in the face of ongoing perturbations.
