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Stabilization of dynamics of oscillatory systems by nonautonomous perturbation

Maxime Lucas1,2,*, Julian Newman1,†, and Aneta Stefanovska1,‡

  • 1Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
  • 2INFN and CSDC, Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Firenze, Italy

  • *m.lucas@lancaster.ac.uk
  • †j.newman1@lancaster.ac.uk
  • ‡aneta@lancaster.ac.uk
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Phys. Rev. E 97, 042209 – Published 17 April, 2018

DOI: https://doi.org/10.1103/PhysRevE.97.042209

Abstract

Synchronization 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, counterintuitively, 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 synchronization 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 stabilization phenomenon is numerically observed. Our findings help support the case that in general, deterministic nonautonomous perturbation is a very good candidate for stabilizing complex dynamics.

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Phys. Rev. E 97, 042209– Published 17 April, 2018
  • Received 24 April 2017
  • Revised 7 March 2018
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