Stabilisation of dynamics of oscillatory systems by non-autonomous perturbation

Abstract

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.

arXiv commentto be published in Phys. Rev. E

References in corpus (10)

• Tipping points in open systems: bifurcation, noise-induced and rate-dependent examples in the climate system
• Coupling functions: Universal insights into dynamical interaction mechanisms
• Analytical and Numerical Studies of Noise-induced Synchronization of Chaotic Systems
• Stochastic models of gene transcription with upstream drives: exact solution and sample path characterization
• The Kuramoto Model with Time-Varying Parameters
• Detecting synchronization of self-sustained oscillators by external driving with varying frequency
• Is the astronomical forcing a reliable and unique pacemaker for climate? A conceptual model study
• Adapting to a Changing Environment: Non-obvious Thresholds in Multi-Scale Systems
• High-order synchronization, transitions, and competition among Arnold tongues in a rotator under harmonic forcing
• Generalized chronotaxic systems: time-dependent oscillatory dynamics stable under continuous perturbation

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