Spatiotemporal chaos collapses to either a rest state or a propagating pulse in a ring network of diffusively coupled, excitable Morris–Lecar neurons. Adding global varying synaptic coupling to the ring network reveals complex transient behavior. Spatiotemporal chaos collapses into a transient pulse that reinitiates spatiotemporal chaos to allow sequential pattern switching until a collapse to the rest state. A domain of irregular neuron activity coexists with a domain of inactive neurons forming a transient chimeralike state. Transient spatial localization of the chimeralike state is observed for stronger synapses.
REFERENCES
1.
T.
Tél
and Y. C.
Lai
, “Chaotic transients in spatially extended systems
,” Phys. Rep.
460
, 245
(2008
). 2.
T. J.
Kaper
, M. A.
Kramer
, and H. G.
Rotstein
, “Focus issue: Rhythms and dynamic transitions in neurological disease: Modeling, computation, and experiment
,” Chaos
23
, 046001
(2013
). 3.
H.
Fujii
and I.
Tsuda
, “Neocortical gap junction-coupled interneuron systems may induce chaotic behavior itinerant among quasi-attractors exhibiting transient synchrony
,” Neurocomputing
58–60
, 151
(2004
). 4.
J.
Lee
, B.
Ermentrout
, and M.
Bodner
, “From cognitive networks to seizures: Stimulus evoked dynamics in a coupled cortical network
,” Chaos
23
, 043111
(2013
). 5.
M. A.
Dahlem
and E. P.
Chronicle
, “A computational perspective on migraine aura
,” Prog. Neurobiol.
74
, 351
(2004
). 6.
M. C.
Cross
and P. C.
Hohenberg
, “Pattern formation outside of equilibrium
,” Rev. Mod. Phys.
65
, 851
(1993
). 7.
S.
Kraut
and U.
Feudel
, “Multistability, noise and attractor hopping: The crucial role of chaotic saddles
,” Phys. Rev. E
66
, 015207(R)
(2002
). 8.
M. I.
Rabinovich
and P.
Varona
, “Robust transient dynamics and brain functions
,” Front. Comput. Neurosci.
5
, 24
(2011
). 9.
S.
Jahnke
, R. M.
Memmesheimer
, and M.
Timme
, “Stable irregular dynamics in complex neural networks
,” Phys. Rev. Lett.
100
, 048102
(2008
). 10.
R.
Zillmer
, N.
Brunel
, and D.
Hansel
, “Very long transients, irregular firing, and chaotic dynamics in networks of randomly connected inhibitory integrate-and-fire neurons
,” Phys. Rev. E
79
, 031909
(2009
). 11.
S.
Luccioli
and A.
Politi
, “Irregular collective behavior of heterogeneous neural networks
,” Phys. Rev. Lett.
105
, 158104
(2010
). 12.
F.
Schittler Neves
and M.
Timme
, “Computation by switching in complex networks of states
,” Phys. Rev. Lett.
109
, 018701
(2012
). 13.
H.-L.
Zou
, Y.
Katori
, Z.-C.
Deng
, K.
Aihara
, and Y.-C.
Lai
, “Controlled generation of switching dynamics among metastable states in pulse-coupled oscillator networks
,” Chaos
25
, 103109
(2015
). 14.
J.
Lafranceschina
and R.
Wackerbauer
, “Impact of weak excitatory synapses on chaotic transients in a diffusively coupled Morris-Lecar neuronal network
,” Chaos
25
, 013119
(2015
). 15.
G.
Ansmann
, K.
Lehnertz
, and U.
Feudel
, “Self-induced switchings between multiple space-time patterns on complex networks of excitable units
,” Phys. Rev. X
6
, 011030
(2016
). 16.
Y. C.
Lai
and T.
Tél
, Transient Chaos: Complex Dynamics on Finite Time Scales, Applied Mathematical Sciences (Springer, New York, 2011).17.
A.
Wacker
, S.
Bose
, and E.
Schöll
, “Transient spatio-temporal chaos in a reaction-diffusion model
,” Europhys. Lett.
31
, 257
(1995
). 18.
M. C.
Strain
and H. S.
Greenside
, “Size-dependent transition to high-dimensional chaotic dynamics in a two-dimensional excitable medium
,” Phys. Rev. Lett.
80
, 2306
(1998
). 19.
R.
Wackerbauer
and K.
Showalter
, “Collapse of spatiotemporal chaos
,” Phys. Rev. Lett.
91
, 174103
(2003
). 20.
K.
Keplinger
and R.
Wackerbauer
, “Transient spatiotemporal chaos in the Morris-Lecar neuronal ring network
,” Chaos
24
, 013126
(2014
). 21.
H.
Hartle
and R.
Wackerbauer
, “Transient chaos and associated system-intrinsic switching of spacetime patterns in two synaptically coupled layers of Morris-Lecar neurons
,” Phys. Rev. E
96
, 032223
(2017
). 22.
B.
Hof
, J.
Westerweel
, T. M.
Schneider
, and B.
Eckhardt
, “Finite lifetime of turbulence in shear flows
,” Nature
443
, 59
(2006
). 23.
D.
Ruelle
, Chaotic Evolution and Strange Attractors
(Cambridge University Press
, New York
, 1989
).24.
M. P.
Fishman
and D. A.
Egolf
, “Revealing the building blocks of spatiotemporal chaos: Deviations from extensivity
,” Phys. Rev. Lett.
96
, 054103
(2006
). 25.
D.
Stahlke
and R.
Wackerbauer
, “Length scale of interaction in spatiotemporal chaos
,” Phys. Rev. E
83
, 046204
(2011
). 26.
D.
Stahlke
and R.
Wackerbauer
, “Transient spatiotemporal chaos is extensive in three reaction-diffusion networks
,” Phys. Rev. E
80
, 056211
(2009
). 27.
R.
Wackerbauer
, “Master stability analysis in transient spatiotemporal chaos
,” Phys. Rev. E
76
, 056207
(2007
). 28.
J. P.
Crutchfield
and K.
Kaneko
, “Are attractors relevant to turbulence
,” Phys. Rev. Lett.
60
, 2715
(1988
). 29.
R.
Wackerbauer
and S.
Kobayashi
, “Noise can delay and advance the collapse of spatiotemporal chaos
,” Phys. Rev. E
75
, 066209
(2007
). 30.
S.
Yonker
and R.
Wackerbauer
, “Nonloncal coupling can prevent the collapse of spatiotemporal chaos
,” Phys. Rev. E
73
, 026218
(2006
). 31.
R.
Wackerbauer
, H.
Sun
, and K.
Showalter
, “Self-segregation of competitive chaotic populations
,” Phys. Rev. Lett.
84
, 5018
(2000
). 32.
Y.
Kuramoto
and D.
Battogtokh
, “Coexistence of coherence and incoherence in nonlocally coupled phase oscillators
,” 5
, 380
(2002
).33.
D. M.
Abrams
and S. H.
Strogatz
, “Chimera states for coupled oscillators
,” Phys. Rev. Lett.
93
, 174102
(2004
). 34.
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
(2012
). 35.
V. M.
Bastidas
, I.
Omelchenko
, A.
Zakharova
, E.
Schöll
, and T.
Brandes
, “Quantum signatures of chimera states
,” Phys. Rev. E
92
, 062924
(2015
). 36.
M. R.
Tinsley
, S.
Nkomo
, and K.
Showalter
, “Chimera and phase-cluster states in populations of coupled chemical oscillators
,” Nat. Phys.
8
, 662
(2012
). 37.
M.
Wickramasinghe
and I. Z.
Kiss
, “Spatially organized dynamical states in chemical oscillator networks: Synchronization, differentiation, and chimera patterns
,” PLoS One
8
, e80586
(2013
). 38.
E. M. E.
Arumugam
and M. L.
Spano
, “A chimeric path to neuronal synchronization
,” Chaos
25
, 013107
(2015
). 39.
M.
Wolfrum
and O. E.
Omel’chenko
, “Chimera states are chaotic transients
,” Phys. Rev. E
84
, 015201
(2011
). 40.
S. W.
Haugland
, L.
Schmidt
, and K.
Krischer
, “Self-organized alternating chimera states in oscillatory media
,” Nat. Sci. Rep.
5
, 9883
(2015
). 41.
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
). 42.
B. K.
Bera
, D.
Ghosh
, and T.
Banerjee
, “Imperfect traveling chimera states induced by local synaptic gradient coupling
,” Phys. Rev. E
94
, 012215
(2016
). 43.
S.
Majhi
, M.
Perc
, and D.
Ghosh
, “Chimera states in uncoupled neurons induced by a multilayer structure
,” Nat. Sci. Rep.
6
, 39033
(2016
). 44.
C.
Bick
, M.
Sebek
, R.
Tönjes
, and I. Z.
Kiss
, “Robust weak chimeras in oscillator networks with delayed linear and quadratic coupling
,” Phys. Rev. Lett.
119
, 168301
(2017
). 45.
F. P.
Kemeth
, S. W.
Haugland
, L.
Schmidt
, I. G.
Kevrekidis
, and K.
Krischer
, “A classification scheme for chimera states
,” Chaos
26
, 094815
(2016
). 46.
E. A.
Martens
, M. J.
Panaggio
, and D. M.
Abrams
, “Basins of attraction for chimera states
,” New J. Phys.
18
, 022002
(2016
). 47.
V.
Santos
, J. D.
Szezech
, A. M.
Batista
, K. C.
Iarosz
, M. S.
Baptista
, H. P.
Ren
, C.
Grebogi
, R. L.
Viana
, I. L.
Caldas
, Y. L.
Maistrenko
, and K.
Kurths
, “Riddling: Chimera’s dilemma
,” Chaos
28
, 081105
(2018
). 48.
A. E.
Botha
and M. R.
Kolahchi
, “Analysis of chimera states as drive-response systems
,” Nat. Sci. Rep.
8
, 1830
(2018
). 49.
N. C.
Rattenborg
, “Behavioral, neurophysiological and evolutionary perspectives on unihemispheric sleep
,” Neurosci. Biobehav. Rev.
24
, 817
(2000
). 50.
R. G.
Andrzejak
, C.
Rummel
, F.
Mormann
, and K.
Schindler
, “All together now: Analogies between chimera state collapses and epileptic seizures
,” Nat. Sci. Rep.
6
, 23000
(2016
). 51.
S.
Majhi
, B. K.
Bera
, D.
Ghosh
, and M.
Perc
, “Chimera states in neuronal networks: A review
,” Phys. Life Rev.
(in press).52.
H.
Sakaguchi
, “Instability of synchronized motion in nonlocally coupled neural oscillators
,” Phys. Rev. E
73
, 031907
(2006
). 53.
T. A.
Glaze
, S.
Lewis
, and S.
Bahar
, “Chimera states in a Hodgkin-Huxley model of thermally sensitive neurons
,” Chaos
26
, 083119
(2016
). 54.
G.
Argyropoulos
, T.
Kasimatis
, and A.
Provata
, “Chimera patterns and subthreshold oscillations in two-dimensional networks of fractally coupled leaky integrate-and-fire neurons
,” Phys. Rev. E
99
, 022208
(2019
). 55.
N.
Semenova
, A.
Zakharova
, V.
Anishchenko
, and E.
Schöll
, “Coherence-resonance chimeras in a network of excitable elements
,” Phys. Rev. Lett.
117
, 014102
(2016
). 56.
C.
Morris
and H.
Lecar
, “Voltage oscillations in the barnacle giant muscle fiber
,” Biophys. J.
35
, 193
(1981
). 57.
K.
Tsumoto
, H.
Kitajima
, T.
Yoshinaga
, K.
Aihara
, and H.
Kawakami
, “Bifurcations in Morris-Lecar neuron model
,” Neurocomputing
69
, 293
(2006
). 58.
G. B.
Ermentrout
and D. H.
Terman
, Mathematical Foundations of Neuroscience, Interdisciplinary Applied Mathematics (Springer, New York, 2010).59.
A.
Destexhe
, Z. F.
Mainen
, and T. J.
Sejnowski
, “Synthesis of models for excitable membranes, synaptic transmission and neuromodulation using a common kinetic formalism
,” J. Comput. Neurosci.
1
, 195
(1994
). 60.
G.
Benettin
, L.
Galgani
, and J.-M.
Strelcyn
, “Kolmogorov entropy and numerical experiments
,” Phys. Rev. A
14
, 2338
(1976
). 61.
The numerical calculation60 of uses a renormalization time interval of and an initial trajectory separation of . A total of renormalizations were calculated to reach convergence; the average of the last measurements determine and standard deviation.
62.
A simulation runs until the STC dynamics collapses to a rest or to a pulse state, or until the computation time of is reached, or until the system behavior was locked for . In that case, the lifetime represents the time before pattern is locked for more than .
63.
M. I.
Rabinovich
and P.
Varona
, “Robust transient dynamics and brain functions
,” Front. Comput. Neurosci.
5
, 24
(2011
). 64.
O.
Mazor
and G.
Laurent
, “Transient dynamics versus fixed points in odor representations by locust antennal lobe projection neurons
,” Neuron
48
, 661
(2005
). 65.
C. R.
Laing
and C. C.
Chow
, “Stationary bumps in networks of spiking neurons
,” Neural Comput.
13
, 1473
(2001
). 66.
C. R.
Laing
, “Bumps in small-world networks
,” Front. Comput. Neurosci.
10
, 53
(2016
). 67.
T. P.
Vogels
, H.
Sprekeler
, F.
Zenke
, C.
Clopath
, and W.
Gerstner
, “Inhibitory plasticity balances excitation and inhibition in sensory pathways and memory networks
,” Science
334
, 1569
(2011
). © 2019 Author(s).
2019
Author(s)
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