PMID: 22587164May 17, 2012Paper

Stationary patterns of coherence and incoherence in two-dimensional arrays of non-locally-coupled phase oscillators

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Oleh E Omel'chenkoO Sudakov

Abstract

Recently, it has been shown that large arrays of identical oscillators with nonlocal coupling can have a remarkable type of solutions that display a stationary macroscopic pattern of coexisting regions with coherent and incoherent motions, often called chimera states. Here, we present a detailed numerical study of the appearance of such solutions in two-dimensional arrays of coupled phase oscillators. We discover a variety of stationary patterns, including circular spots, stripe patterns, and patterns of multiple spirals. Here, stationarity means that, for increasing system size, the locally averaged phase distributions tend to the stationary profile given by the corresponding thermodynamic limit equation.

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Citations

Jul 6, 2014·Chaos·Oleh E Omel'chenkoCarlo R Laing
Sep 10, 2015·Scientific Reports·Nan YaoYing-Cheng Lai
Sep 4, 2015·Chaos·Iryna OmelchenkoEckehard Schöll
Nov 3, 2017·Chaos·Sarika JalanBibhabasu Patra
Jan 20, 2018·Physical Review. E·Changhai TianZonghua Liu
Dec 30, 2017·Physical Review Letters·Zachary G NicolaouAdilson E Motter
Mar 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Iryna OmelchenkoPhilipp Hövel
Feb 13, 2016·Physical Review. E·Mark J PanaggioCarlo R Laing
Mar 18, 2016·Physical Review. E·Thomas IselePhilipp Hövel
Jul 3, 2020·Chaos·Volodymyr MaistrenkoOleksiy Osiv
Sep 19, 2020·Physical Review. E·Nikita KrukHeinz Koeppl
Mar 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Patrycja JarosTomasz Kapitaniak
Mar 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Mark J Panaggio, Daniel M Abrams
May 10, 2020·Scientific Reports·Jan Frederik TotzKenneth Showalter
Nov 14, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Jianbo XieHsien-Ching Kao
May 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Fabian BöhmKathy Lüdge
Jun 15, 2016·Physical Review. E·M G ClercR G Rojas
Feb 20, 2019·Physical Review. E·Nan YaoYing-Cheng Lai
Oct 9, 2019·Scientific Reports·Ling KangZonghua Liu
Apr 2, 2016·Physical Review Letters·Iryna OmelchenkoEckehard Schöll
Feb 17, 2018·Physical Review. E·Iryna OmelchenkoEckehard Schöll
Dec 7, 2018·Chaos·Tanmoy BanerjeeAnna Zakharova
Jun 17, 2018·Physical Review. E·T KasimatisA Provata
Feb 13, 2016·Physical Review. E·Bidesh K BeraM Lakshmanan
Dec 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Carlo R Laing
Aug 31, 2016·Physical Review. E·Hon Wai Lau, Jörn Davidsen
Apr 19, 2017·Physical Review. E·Alexander SchmidtPhilipp Hövel
Mar 19, 2013·Physical Review Letters·Mark J Panaggio, Daniel M Abrams
Jun 19, 2013·Physical Review Letters·Iryna OmelchenkoEckehard Schöll
Oct 15, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Dawid DudkowskiTomasz Kapitaniak
Mar 4, 2014·Physical Review Letters·Jan SieberMatthias Wolfrum
Aug 21, 2013·Physical Review Letters·Laurent LargerYuri Maistrenko

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