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Title: Stability of entrainment of a continuum of coupled oscillators

Abstract

Complex natural and engineered systems are ubiquitous, and their behavior is challenging to characterize and control. Here, we examine the design of the entrainment process for an uncountably infinite collection of coupled phase oscillators that are all subject to the same periodic driving signal. In the absence of coupling, an appropriately designed input can result in each oscillator attaining the frequency of the driving signal, with a phase offset determined by its natural frequency. We also consider a special case of interacting oscillators in which the coupling tends to destabilize the phase configuration to which the driving signal would send the collection in the absence of coupling. In this setting, we derive stability results that characterize the trade-off between the effects of driving and coupling, and compare these results to the well-known Kuramoto model of a collection of free-running coupled oscillators.

Authors:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [2]
  1. Univ. of California, Davis, CA (United States). Dept. of Mathematics
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Applied Mathematics and Plasma Physics
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1408843
Alternate Identifier(s):
OSTI ID: 1398105
Report Number(s):
LA-UR-17-26419
Journal ID: ISSN 1054-1500
Grant/Contract Number:
AC52-06NA25396; W911NF-13-1-0340; W911NF-09-2-0053
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Chaos: An Interdisciplinary Journal of Nonlinear Science
Additional Journal Information:
Journal Volume: 27; Journal Issue: 10; Journal ID: ISSN 1054-1500
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING; Mathematics

Citation Formats

Snyder, Jordan, Zlotnik, Anatoly, and Hagberg, Aric. Stability of entrainment of a continuum of coupled oscillators. United States: N. p., 2017. Web. doi:10.1063/1.4994567.
Snyder, Jordan, Zlotnik, Anatoly, & Hagberg, Aric. Stability of entrainment of a continuum of coupled oscillators. United States. doi:10.1063/1.4994567.
Snyder, Jordan, Zlotnik, Anatoly, and Hagberg, Aric. Thu . "Stability of entrainment of a continuum of coupled oscillators". United States. doi:10.1063/1.4994567.
@article{osti_1408843,
title = {Stability of entrainment of a continuum of coupled oscillators},
author = {Snyder, Jordan and Zlotnik, Anatoly and Hagberg, Aric},
abstractNote = {Complex natural and engineered systems are ubiquitous, and their behavior is challenging to characterize and control. Here, we examine the design of the entrainment process for an uncountably infinite collection of coupled phase oscillators that are all subject to the same periodic driving signal. In the absence of coupling, an appropriately designed input can result in each oscillator attaining the frequency of the driving signal, with a phase offset determined by its natural frequency. We also consider a special case of interacting oscillators in which the coupling tends to destabilize the phase configuration to which the driving signal would send the collection in the absence of coupling. In this setting, we derive stability results that characterize the trade-off between the effects of driving and coupling, and compare these results to the well-known Kuramoto model of a collection of free-running coupled oscillators.},
doi = {10.1063/1.4994567},
journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science},
number = 10,
volume = 27,
place = {United States},
year = {Thu Oct 05 00:00:00 EDT 2017},
month = {Thu Oct 05 00:00:00 EDT 2017}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on October 5, 2018
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