Chimera-like states are manifested through the coexistence of synchronous and asynchronous dynamics and have been observed in various systems. To analyze the role of network topology in giving rise to chimera-like states, we study a heterogeneous network model comprising two groups of nodes, of high and low degrees of connectivity. The architecture facilitates the analysis of the system, which separates into a densely connected coherent group of nodes, perturbed by their sparsely connected drifting neighbors. It describes a synchronous behavior of the densely connected group and scaling properties of the induced perturbations.
References
1.
J. A.
Acebrón
, L. L.
Bonilla
, C. J. P.
Vicente
, F.
Ritort
, and R.
Spigler
, “The Kuramoto model: A simple paradigm for synchronization phenomena
,” Rev. Mod. Phys.
77
, 137
–185
(2005
).2.
S.
Boccaletti
, J.
Kurths
, G.
Osipov
, D. L.
Valladares
, and C. S.
Zhou
, “The synchronization of chaotic systems
,” Phys. Rep.
366
(1–2
), 1
–101
(2002
).3.
F. A.
Rodrigues
, T. K. D. M.
Peron
, P.
Ji
, and J.
Kurths
, “The Kuramoto model in complex networks
,” Phys. Rep.
610
, 1
–98
(2016
).4.
M. J.
Panaggio
and D. M.
Abrams
, “Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
,” Nonlinearity
28
(3
), R67
(2015
).5.
Y.
Zhu
, Z.
Zheng
, and J.
Yang
, “Chimera states on complex networks
,” Phys. Rev. E
89
, 022914
(2014
).6.
Y.
Kuramoto
and D.
Battogtokh
, “Coexistence of coherence and incoherence in nonlocally coupled phase oscillators
,” Nonlinear Phenom. Complex Syst.
5
(4
), 380
–385
(2002
).7.
S.-I.
Shima
and Y.
Kuramoto
, “Rotating spiral waves with phase-randomized core in nonlocally coupled oscillators
,” Phys. Rev. E
69
, 036213
(2004
).8.
D. M.
Abrams
and S. H.
Strogatz
, “Chimera states for coupled oscillators
,” Phys. Rev. Lett.
93
, 174102
(2004
).9.
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
).10.
P.
Ashwin
and O.
Burylko
, “Weak chimeras in minimal networks of coupled phase oscillators
,” Chaos
25
(1
), 013106
(2015
).11.
C.
Bick
, “Isotropy of angular frequencies and weak chimeras with broken symmetry
,” J. Nonlinear Sci.
27
, 605
–626
(2017
).12.
D.
Saad
and A.
Mozeika
, “Emergence of equilibriumlike domains within nonequilibrium ising spin systems
,” Phys. Rev. E
87
, 032131
(2013
).13.
E.
Ott
and T. M.
Antonsen
, “Low dimensional behavior of large systems of globally coupled oscillators
,” Chaos
18
(3
), 037113
(2008
).14.
E. A.
Martens
, M. J.
Panaggio
, and D. M.
Abrams
, “Basins of attraction for chimera states
,” New J. Phys.
18
(2
), 022002
(2016
).15.
M. R.
Tinsley
, S.
Nkomo
, and K.
Showalter
, “Chimera and phase-cluster states in populations of coupled chemical oscillators
,” Nat. Phys.
8
(9
), 662
–665
(2012
).16.
A. M.
Hagerstrom
, T. E.
Murphy
, R.
Roy
, P.
Hovel
, I.
Omelchenko
, and E.
Scholl
, “Experimental observation of chimeras in coupled-map lattices
,” Nat. Phys.
8
(9
), 658
–661
(2012
).17.
E. A.
Martens
, S.
Thutupalli
, A.
Fourrière
, and O.
Hallatschek
, “Chimera states in mechanical oscillator networks
,” Proc. Natl. Acad. Sci.
110
(26
), 10563
–10567
(2013
).18.
T.
Kapitaniak
, P.
Kuzma
, J.
Wojewoda
, K.
Czolczynski
, and Y.
Maistrenko
, “Imperfect chimera states for coupled pendula
,” Sci. Rep.
4
, 6379
(2014
).19.
S. H.
Strogatz
, “Exploring complex networks
,” Nature
410
(6825
), 268
–276
(2001
).20.
R.
Albert
and A.-L.
Barabási
, “Statistical mechanics of complex networks
,” Rev. Mod. Phys.
74
, 47
–97
(2002
).21.
A.
Arenas
, A.
Díaz-Guilera
, J.
Kurths
, Y.
Moreno
, and C.
Zhou
, “Synchronization in complex networks
,” Phys. Rep.
469
(3
), 93
–153
(2008
).22.
V.
Vuksanović
and P.
Hövel
, “Functional connectivity of distant cortical regions: Role of remote synchronization and symmetry in interactions
,” NeuroImage
97
, 1
–8
(2014
).23.
J.
Hizanidis
, N. E.
Kouvaris
, G.
Zamora-López
, A.
Díaz-Guilera
, and C. G.
Antonopoulos
, “Chimera-like states in modular neural networks
,” Sci. Rep.
6
, 19845
(2016
).24.
T.-W.
Ko
and G. B.
Ermentrout
, “Partially locked states in coupled oscillators due to inhomogeneous coupling
,” Phys. Rev. E
78
, 016203
(2008
).25.
C. R.
Laing
, “Chimera states in heterogeneous networks
,” Chaos
19
(1
), 013113
(2009
).26.
C. R.
Laing
, “The dynamics of chimera states in heterogeneous kuramoto networks
,” Phys. D: Nonlinear Phenom.
238
(16
), 1569
–1588
(2009
).27.
C. R.
Laing
, K.
Rajendran
, and I. G.
Kevrekidis
, “Chimeras in random non-complete networks of phase oscillators
,” Chaos
22
(1
), 013132
(2012
).28.
I.
Omelchenko
, A.
Provata
, J.
Hizanidis
, E.
Schöll
, and P.
Hövel
, “Robustness of chimera states for coupled fitzhugh-nagumo oscillators
,” Phys. Rev. E
91
, 022917
(2015
).29.
A.
Buscarino
, M.
Frasca
, L. V.
Gambuzza
, and P.
Hövel
, “Chimera states in time-varying complex networks
,” Phys. Rev. E
91
, 022817
(2015
).30.
X.
Jiang
and D. M.
Abrams
, “Symmetry-broken states on networks of coupled oscillators
,” Phys. Rev. E
93
, 052202
(2016
).31.
S.
Olmi
and A.
Torcini
, Chimera States in Pulse Coupled Neural Networks: The Influence of Dilution and Noise
e-print arXiv:1606.08618 (2017
).32.
C.
Zhou
and J.
Kurths
, “Hierarchical synchronization in complex networks with heterogeneous degrees
,” Chaos
16
(1
), 015104
(2006
).33.
J.
Gómez-Gardeñes
, Y.
Moreno
, and A.
Arenas
, “Paths to synchronization on complex networks
,” Phys. Rev. Lett.
98
, 034101
(2007
).34.
J.
Gómez-Gardeñes
, S.
Gómez
, A.
Arenas
, and Y.
Moreno
, “Explosive synchronization transitions in scale-free networks
,” Phys. Rev. Lett.
106
, 128701
(2011
).35.
T.
Pereira
, “Hub synchronization in scale-free networks
,” Phys. Rev. E
82
, 036201
(2010
).36.
J.-P.
Eckmann
, E.
Moses
, O.
Stetter
, T.
Tlusty
, and C.
Zbinden
, “Leaders of neuronal cultures in a quorum percolation model
,” Front. Comput. Neurosci.
4
, 132
(2010
).37.
P. S.
Skardal
, D.
Taylor
, J.
Sun
, and A.
Arenas
, “Erosion of synchronization in networks of coupled oscillators
,” Phys. Rev. E
91
, 010802
(2015
).38.
Y.
Kuramoto
, Chemical Oscillations, Waves, and Turbulence
(Springer-Verlag
, Berlin/Heidelberg
, 1984
).39.
P. S.
Skardal
, D.
Taylor
, J.
Sun
, and A.
Arenas
, “Erosion of synchronization: Coupling heterogeneity and network structure
,” Phys. D: Nonlinear Phenom.
323–324
, 40
–48
(2016
).© 2017 Author(s).
2017
Author(s)
You do not currently have access to this content.