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Stabilization of dynamics of oscillatory systems by nonautonomous perturbation

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Stabilization of dynamics of oscillatory systems by nonautonomous perturbation. / Lucas, Maxime; Newman, Julian; Stefanovska, Aneta.

In: Physical Review E, Vol. 97, No. 4, 042209, 17.04.2018.

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@article{982fc1ab1b744eb28babc81baa2ec19a,
title = "Stabilization of dynamics of oscillatory systems by nonautonomous perturbation",
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.",
author = "Maxime Lucas and Julian Newman and Aneta Stefanovska",
year = "2018",
month = apr
day = "17",
doi = "10.1103/PhysRevE.97.042209",
language = "English",
volume = "97",
journal = "Physical Review E",
issn = "1539-3755",
publisher = "American Physical Society",
number = "4",

}

RIS

TY - JOUR

T1 - Stabilization of dynamics of oscillatory systems by nonautonomous perturbation

AU - Lucas, Maxime

AU - Newman, Julian

AU - Stefanovska, Aneta

PY - 2018/4/17

Y1 - 2018/4/17

N2 - 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.

AB - 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.

U2 - 10.1103/PhysRevE.97.042209

DO - 10.1103/PhysRevE.97.042209

M3 - Journal article

VL - 97

JO - Physical Review E

JF - Physical Review E

SN - 1539-3755

IS - 4

M1 - 042209

ER -