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Title: Regular and irregular patterns of self-localized excitation in arrays of coupled phase oscillators

Abstract

We study a system of phase oscillators with nonlocal coupling in a ring that supports self-organized patterns of coherence and incoherence, called chimera states. Introducing a global feedback loop, connecting the phase lag to the order parameter, we can observe chimera states also for systems with a small number of oscillators. Numerical simulations show a huge variety of regular and irregular patterns composed of localized phase slipping events of single oscillators. Using methods of classical finite dimensional chaos and bifurcation theory, we can identify the emergence of chaotic chimera states as a result of transitions to chaos via period doubling cascades, torus breakup, and intermittency. We can explain the observed phenomena by a mechanism of self-modulated excitability in a discrete excitable medium.

Authors:
;  [1];  [2]
  1. Weierstrass Institute, Mohrenstrasse 39, Berlin 10117 (Germany)
  2. College of Engineering, Mathematics and Physical Sciences, University of Exeter, North Park Road, Exeter EX4 4QF (United Kingdom)
Publication Date:
OSTI Identifier:
22402559
Resource Type:
Journal Article
Journal Name:
Chaos (Woodbury, N. Y.)
Additional Journal Information:
Journal Volume: 25; Journal Issue: 5; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1054-1500
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BIFURCATION; CHAOS THEORY; CHIMERAS; COMPUTERIZED SIMULATION; COUPLING; EXCITATION; FEEDBACK; NONLOCAL POTENTIAL; ORDER PARAMETERS; OSCILLATORS; PHASE OSCILLATIONS

Citation Formats

Wolfrum, Matthias, Omel'chenko, Oleh E., and Sieber, Jan. Regular and irregular patterns of self-localized excitation in arrays of coupled phase oscillators. United States: N. p., 2015. Web. doi:10.1063/1.4921297.
Wolfrum, Matthias, Omel'chenko, Oleh E., & Sieber, Jan. Regular and irregular patterns of self-localized excitation in arrays of coupled phase oscillators. United States. doi:10.1063/1.4921297.
Wolfrum, Matthias, Omel'chenko, Oleh E., and Sieber, Jan. Fri . "Regular and irregular patterns of self-localized excitation in arrays of coupled phase oscillators". United States. doi:10.1063/1.4921297.
@article{osti_22402559,
title = {Regular and irregular patterns of self-localized excitation in arrays of coupled phase oscillators},
author = {Wolfrum, Matthias and Omel'chenko, Oleh E. and Sieber, Jan},
abstractNote = {We study a system of phase oscillators with nonlocal coupling in a ring that supports self-organized patterns of coherence and incoherence, called chimera states. Introducing a global feedback loop, connecting the phase lag to the order parameter, we can observe chimera states also for systems with a small number of oscillators. Numerical simulations show a huge variety of regular and irregular patterns composed of localized phase slipping events of single oscillators. Using methods of classical finite dimensional chaos and bifurcation theory, we can identify the emergence of chaotic chimera states as a result of transitions to chaos via period doubling cascades, torus breakup, and intermittency. We can explain the observed phenomena by a mechanism of self-modulated excitability in a discrete excitable medium.},
doi = {10.1063/1.4921297},
journal = {Chaos (Woodbury, N. Y.)},
issn = {1054-1500},
number = 5,
volume = 25,
place = {United States},
year = {2015},
month = {5}
}