2018/03/30 by Maxime Lucas, Julian Newman, Aneta Stefanovska · 1 citation
Physics and Astronomy · #nlin.AO
paper · pdf · doi:10.1103/physreve.97.042209
to be published in Phys. Rev. E
arxiv created 2018/03/30 · arxiv updated 2018/05/09
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.