We present a universal characterization scheme for chimera states applicable to both numerical and experimental data sets. The scheme is based on two correlation measures that enable a meaningful definition of chimera states as well as their classification into three categories: stationary, turbulent, and breathing. In addition, these categories can be further subdivided according to the time-stationarity of these two measures. We demonstrate that this approach is both consistent with previously recognized chimera states and enables us to classify states as chimeras which have not been categorized as such before. Furthermore, the scheme allows for a qualitative and quantitative comparison of experimental chimeras with chimeras obtained through numerical simulations.
References
1.
Y.
Kuramoto
and D.
Battogtokh
, “Coexistence of coherence and incoherence in nonlocally coupled phase oscillators
,” Nonlinear Phenom. Complex Syst.
5
, 380
–385
(2002
).2.
D. M.
Abrams
and S. H.
Strogatz
, “Chimera states for coupled oscillators
,” Phys. Rev. Lett.
93
, 174102
(2004
).3.
C. R.
Laing
and C. C.
Chow
, “Stationary bumps in networks of spiking neurons
,” Neural Comput.
13
, 1473
–1494
(2001
).4.
N.
Rattenborg
, C.
Amlaner
, and S.
Lima
, “Behavioral, neurophysiological and evolutionary perspectives on unihemispheric sleep
,” Neurosci. Biobehav. Rev.
24
, 817
–842
(2000
).5.
D.
Barkley
and L. S.
Tuckerman
, “Computational study of turbulent laminar patterns in Couette flow
,” Phys. Rev. Lett.
94
, 014502
(2005
).6.
Y.
Duguet
and P.
Schlatter
, “Oblique laminar-turbulent interfaces in plane shear flows
,” Phys. Rev. Lett.
110
, 034502
(2013
).7.
G.
Bordyugov
, A.
Pikovsky
, and M.
Rosenblum
, “Self-emerging and turbulent chimeras in oscillator chains
,” Phys. Rev. E
82
, 035205
(2010
).8.
A. M.
Hagerstrom
, T. E.
Murphy
, R.
Roy
, P.
Hövel
, I.
Omelchenko
, and E.
Schöll
, “Experimental observation of chimeras in coupled-map lattices
,” Nat. Phys.
8
, 658
–661
(2012
).9.
I.
Omelchenko
, Y.
Maistrenko
, P.
Hövel
, and E.
Schöll
, “Loss of coherence in dynamical networks: Spatial chaos and chimera states
,” Phys. Rev. Lett.
106
, 234102
(2011
).10.
G. C.
Sethia
, A.
Sen
, and G. L.
Johnston
, “Amplitude-mediated chimera states
,” Phys. Rev. E
88
, 042917
(2013
).11.
A.
Zakharova
, M.
Kapeller
, and E.
Schöll
, “Chimera death: Symmetry breaking in dynamical networks
,” Phys. Rev. Lett.
112
, 154101
(2014
).12.
D. M.
Abrams
, R.
Mirollo
, S. H.
Strogatz
, and D. A.
Wiley
, “Solvable model for chimera states of coupled oscillators
,” Phys. Rev. Lett.
101
, 084103
(2008
).13.
M. R.
Tinsley
, S.
Nkomo
, and K.
Showalter
, “Chimera and phase-cluster states in populations of coupled chemical oscillators
,” Nat. Phys.
8
, 662
–665
(2012
).14.
L.
Schmidt
, K.
Schönleber
, K.
Krischer
, and V.
García-Morales
, “Coexistence of synchrony and incoherence in oscillatory media under nonlinear global coupling
,” Chaos
24
, 013102
(2014
).15.
A.
Yeldesbay
, A.
Pikovsky
, and M.
Rosenblum
, “Chimera like states in an ensemble of globally coupled oscillators
,” Phys. Rev. Lett.
112
, 144103
(2014
).16.
E. A.
Martens
, S.
Thutupalli
, A.
Fourrière
, and O.
Hallatschek
, “Chimera states in mechanical oscillator networks
,” Proc. Natl. Acad. Sci. U.S.A.
110
, 10563
–10567
(2013
).17.
D.
Battogtokh
, A.
Preusser
, and A.
Mikhailov
, “Controlling turbulence in the complex Ginzburg-Landau equation II. Two-dimensional systems
,” Phys. D
106
, 327
–362
(1997
).18.
L.
Schmidt
and K.
Krischer
, “Chimeras in globally coupled oscillatory systems: From ensembles of oscillators to spatially continuous media
,” Chaos
25
, 064401
(2015
).19.
M.
Wolfrum
and O. E.
Omel'chenko
, “Chimera states are chaotic transients
,” Phys. Rev. E
84
, 015201
(2011
).20.
P.
Ashwin
and O.
Burylko
, “Weak chimeras in minimal networks of coupled phase oscillators
,” Chaos
25
, 013106
(2015
).21.
L.
Schmidt
and K.
Krischer
, “Clustering as a prerequisite for chimera states in globally coupled systems
,” Phys. Rev. Lett.
114
, 034101
(2015
).22.
M. J.
Panaggio
and D. M.
Abrams
, “Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
,” Nonlinearity
28
, R67
–R87
(2015
).23.
R.
Gopal
, V. K.
Chandrasekar
, A.
Venkatesan
, and M.
Lakshmanan
, “Observation and characterization of chimera states in coupled dynamical systems with nonlocal coupling
,” Phys. Rev. E
89
, 052914
(2014
).24.
See supplementary material at http://dx.doi.org/10.1063/1.4959804 for details on the individual systems and on the numerical methods used.
25.
B.
Shraiman
, A.
Pumir
, W.
van Saarloos
, P.
Hohenberg
, H.
Chaté
, and M.
Holen
, “Spatiotemporal chaos in the one-dimensional complex Ginzburg-Landau equation
,” Phys. D
57
, 241
–248
(1992
).26.
S. W.
Haugland
, L.
Schmidt
, and K.
Krischer
, “Self-organized alternating chimera states in oscillatory media
,” Sci. Rep.
5
, 9883
(2015
).27.
S. A. M.
Loos
, J. C.
Claussen
, E.
Schöll
, and A.
Zakharova
, “Chimera patterns under the impact of noise
,” Phys. Rev. E
93
, 012209
(2016
).28.
M.
Falcke
and H.
Engel
, “Influence of global coupling through the gas phase on the dynamics of CO oxidation on Pt(110)
,” Phys. Rev. E
50
, 1353
–1359
(1994
).29.
M.
Falcke
and H.
Engel
, “Pattern formation during the CO oxidation on Pt(110) surfaces under global coupling
,” J. Chem. Phys.
101
, 6255
–6263
(1994
).30.
M.
Falcke
, Strukturbildung in Reaktions- Diffusionssystemen und globale Kopplung
(Wissenschaft und Technik Verlag Gross
, Berlin
, Sebastianstr. 84, 1995
).31.
K.
Schönleber
, C.
Zensen
, A.
Heinrich
, and K.
Krischer
, “Pattern formation during the oscillatory photoelectrodissolution of n-type silicon: Turbulence, clusters and chimeras
,” New J. Phys.
16
, 063024
(2014
).32.
I.
Omelchenko
, O. E.
Omel'chenko
, P.
Hövel
, and E.
Schöll
, “When nonlocal coupling between oscillators becomes stronger: Patched synchrony or multichimera states
,” Phys. Rev. Lett.
110
, 224101
(2013
).33.
I.
Omelchenko
, B.
Riemenschneider
, P.
Hövel
, Y.
Maistrenko
, and E.
Schöll
, “Transition from spatial coherence to incoherence in coupled chaotic systems
,” Phys. Rev. E
85
, 026212
(2012
).© 2016 Author(s).
2016
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