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Symmetry breaking yields chimeras in two small populations of Kuramoto-type oscillators

Burylko, Oleksandr ; Martens, Erik A. LU orcid and Bick, Christian (2022) In Chaos 32(9).
Abstract

Despite their simplicity, networks of coupled phase oscillators can give rise to intriguing collective dynamical phenomena. However, the symmetries of globally and identically coupled identical units do not allow solutions where distinct oscillators are frequency-unlocked - a necessary condition for the emergence of chimeras. Thus, forced symmetry breaking is necessary to observe chimera-type solutions. Here, we consider the bifurcations that arise when full permutational symmetry is broken for the network to consist of coupled populations. We consider the smallest possible network composed of four phase oscillators and elucidate the phase space structure, (partial) integrability for some parameter values, and how the bifurcations away... (More)

Despite their simplicity, networks of coupled phase oscillators can give rise to intriguing collective dynamical phenomena. However, the symmetries of globally and identically coupled identical units do not allow solutions where distinct oscillators are frequency-unlocked - a necessary condition for the emergence of chimeras. Thus, forced symmetry breaking is necessary to observe chimera-type solutions. Here, we consider the bifurcations that arise when full permutational symmetry is broken for the network to consist of coupled populations. We consider the smallest possible network composed of four phase oscillators and elucidate the phase space structure, (partial) integrability for some parameter values, and how the bifurcations away from full symmetry lead to frequency-unlocked weak chimera solutions. Since such solutions wind around a torus they must arise in a global bifurcation scenario. Moreover, periodic weak chimeras undergo a period-doubling cascade leading to chaos. The resulting chaotic dynamics with distinct frequencies do not rely on amplitude variation and arise in the smallest networks that support chaos.

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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Chaos
volume
32
issue
9
article number
093109
publisher
American Institute of Physics (AIP)
external identifiers
  • scopus:85138261450
  • pmid:36182374
ISSN
1054-1500
DOI
10.1063/5.0088465
language
English
LU publication?
yes
additional info
Funding Information: O.B. acknowledges support of the National Research Foundation of Ukraine (Project No. 2020.02/0089). Publisher Copyright: © 2022 Author(s).
id
39294010-ad3a-4d4f-a705-cdf83ed90b12
date added to LUP
2022-10-11 08:53:37
date last changed
2025-03-21 19:02:02
@article{39294010-ad3a-4d4f-a705-cdf83ed90b12,
  abstract     = {{<p>Despite their simplicity, networks of coupled phase oscillators can give rise to intriguing collective dynamical phenomena. However, the symmetries of globally and identically coupled identical units do not allow solutions where distinct oscillators are frequency-unlocked - a necessary condition for the emergence of chimeras. Thus, forced symmetry breaking is necessary to observe chimera-type solutions. Here, we consider the bifurcations that arise when full permutational symmetry is broken for the network to consist of coupled populations. We consider the smallest possible network composed of four phase oscillators and elucidate the phase space structure, (partial) integrability for some parameter values, and how the bifurcations away from full symmetry lead to frequency-unlocked weak chimera solutions. Since such solutions wind around a torus they must arise in a global bifurcation scenario. Moreover, periodic weak chimeras undergo a period-doubling cascade leading to chaos. The resulting chaotic dynamics with distinct frequencies do not rely on amplitude variation and arise in the smallest networks that support chaos.</p>}},
  author       = {{Burylko, Oleksandr and Martens, Erik A. and Bick, Christian}},
  issn         = {{1054-1500}},
  language     = {{eng}},
  month        = {{09}},
  number       = {{9}},
  publisher    = {{American Institute of Physics (AIP)}},
  series       = {{Chaos}},
  title        = {{Symmetry breaking yields chimeras in two small populations of Kuramoto-type oscillators}},
  url          = {{http://dx.doi.org/10.1063/5.0088465}},
  doi          = {{10.1063/5.0088465}},
  volume       = {{32}},
  year         = {{2022}},
}