An outstanding open problem in neuroscience is to understand how neural systems are capable of producing and sustaining complex spatiotemporal dynamics. Computational models that combine local dynamics with in vivo measurements of anatomical and functional connectivity can be used to test potential mechanisms underlying this complexity. We compared two conceptually different mechanisms: noise-driven switching between equilibrium solutions (modeled by coupled Stuart–Landau oscillators) and deterministic chaos (modeled by coupled Rossler oscillators). We found that both models struggled to simultaneously reproduce multiple observables computed from the empirical data. This issue was especially manifested in the case of noise-driven dynamics close to a bifurcation, which imposed overly strong constraints on the optimal model parameters. In contrast, the chaotic model could produce complex behavior over a range of parameters, thus being capable of capturing multiple observables at the same time with good performance. Our observations support the view of the brain as a non-equilibrium system able to produce endogenous variability. We presented a simple model capable of jointly reproducing functional connectivity computed at different temporal scales. Besides adding to our conceptual understanding of brain complexity, our results inform and constrain the future development of biophysically realistic large-scale models.
REFERENCES
1.
Here, we employ the term large-scale as a synonym of brain-wide in reference to macroscopic brain activity spanning from a few centimeters up to the whole cortex.
2.
M. E.
Raichle
, “The brain’s dark energy
,” Science
314
, 1249
(2006
). 3.
G.
Deco
, V. K.
Jirsa
, and A. R.
McIntosh
, “Emerging concepts for the dynamical organization of resting-state activity in the brain
,” Nat. Rev. Neurosci.
12
, 43
–56
(2011
). 4.
M. P.
Van Den Heuvel
and H. E. H.
Pol
, “Exploring the brain network: A review on resting-state fMRI functional connectivity
,” Eur. Neuropsychopharmacol.
20
, 519
–534
(2010
). 5.
J. S.
Damoiseaux
, S.
Rombouts
, F.
Barkhof
, P.
Scheltens
, C. J.
Stam
, S. M.
Smith
, and C. F.
Beckmann
, “Consistent resting-state networks across healthy subjects
,” Proc. Natl. Acad. Sci. U.S.A.
103
, 13848
–13853
(2006
). 6.
S. M.
Smith
, P. T.
Fox
, K. L.
Miller
, D. C.
Glahn
, P. M.
Fox
, C. E.
Mackay
, N.
Filippini
, K. E.
Watkins
, R.
Toro
, A. R.
Laird
et al., “Correspondence of the brain’s functional architecture during activation and rest
,” Proc. Natl. Acad. Sci. U.S.A.
106
, 13040
–13045
(2009
). 7.
G.
Deco
and V. K.
Jirsa
, “Ongoing cortical activity at rest: Criticality, multistability, and ghost attractors
,” J. Neurosci.
32
, 3366
–3375
(2012
). 8.
G.
Deco
, V. K.
Jirsa
, and A. R.
McIntosh
, “Resting brains never rest: Computational insights into potential cognitive architectures
,” Trends Neurosci.
36
, 268
–274
(2013
). 9.
F.
Cavanna
, M. G.
Vilas
, M.
Palmucci
, and E.
Tagliazucchi
, “Dynamic functional connectivity and brain metastability during altered states of consciousness
,” NeuroImage
180
, 383
–395
(2018
). 10.
M. W.
Cole
, T.
Ito
, D. S.
Bassett
, and D. H.
Schultz
, “Activity flow over resting-state networks shapes cognitive task activations
,” Nat. Neurosci.
19
, 1718
–1726
(2016
). 11.
R. M.
Hutchison
, L. S.
Leung
, S. M.
Mirsattari
, J. S.
Gati
, R. S.
Menon
, and S.
Everling
, “Resting-state networks in the macaque at 7 t
,” NeuroImage
56
, 1546
–1555
(2011
). 12.
C. P.
Pawela
, B. B.
Biswal
, Y. R.
Cho
, D. S.
Kao
, R.
Li
, S. R.
Jones
, M. L.
Schulte
, H. S.
Matloub
, A. G.
Hudetz
, and J. S.
Hyde
, “Resting-state functional connectivity of the rat brain
,” Magn. Reson. Med.
59
, 1021
–1029
(2008
). 13.
D.
Szabo
, K.
Czeibert
, Á.
Kettinger
, M.
Gácsi
, A.
Andics
, Á.
Miklósi
, and E.
Kubinyi
, “Resting-state fMRI data of awake dogs (Canis familiaris) via group-level independent component analysis reveal multiple, spatially distributed resting-state networks
,” Sci. Rep.
9
, 15270
(2019
). 14.
Z. C.
Zhou
, A. P.
Salzwedel
, S.
Radtke-Schuller
, Y.
Li
, K. K.
Sellers
, J. H.
Gilmore
, Y.-Y. I.
Shih
, F.
Fröhlich
, and W.
Gao
, “Resting state network topology of the ferret brain
,” NeuroImage
143
, 70
–81
(2016
). 15.
A. M.
Belcher
, C. C.
Yen
, H.
Stepp
, H.
Gu
, H.
Lu
, Y.
Yang
, A. C.
Silva
, and E. A.
Stein
, “Large-scale brain networks in the awake, truly resting marmoset monkey
,” J. Neurosci.
33
, 16796
–16804
(2013
). 16.
F.
Sforazzini
, A. J.
Schwarz
, A.
Galbusera
, A.
Bifone
, and A.
Gozzi
, “Distributed BOLD and CBV-weighted resting-state networks in the mouse brain
,” NeuroImage
87
, 403
–415
(2014
). 17.
A.
Custo
, D.
Van De Ville
, W. M.
Wells
, M. I.
Tomescu
, D.
Brunet
, and C. M.
Michel
, “Electroencephalographic resting-state networks: Source localization of microstates
,” Brain Connect.
7
, 671
–682
(2017
). 18.
M. J.
Brookes
, M.
Woolrich
, H.
Luckhoo
, D.
Price
, J. R.
Hale
, M. C.
Stephenson
, G. R.
Barnes
, S. M.
Smith
, and P. G.
Morris
, “Investigating the electrophysiological basis of resting state networks using magnetoencephalography
,” Proc. Natl. Acad. Sci. U.S.A.
108
, 16783
–16788
(2011
). 19.
C. D.
Hacker
, A. Z.
Snyder
, M.
Pahwa
, M.
Corbetta
, and E. C.
Leuthardt
, “Frequency-specific electrophysiologic correlates of resting state fMRI networks
,” NeuroImage
149
, 446
–457
(2017
). 20.
L.
Duan
, Y.-J.
Zhang
, and C.-Z.
Zhu
, “Quantitative comparison of resting-state functional connectivity derived from fNIRs and fMRI: A simultaneous recording study
,” NeuroImage
60
, 2008
–2018
(2012
). 21.
H.
Laufs
, K.
Krakow
, P.
Sterzer
, E.
Eger
, A.
Beyerle
, A.
Salek-Haddadi
, and A.
Kleinschmidt
, “Electroencephalographic signatures of attentional and cognitive default modes in spontaneous brain activity fluctuations at rest
,” Proc. Natl. Acad. Sci. U.S.A.
100
, 11053
–11058
(2003
). 22.
D.
Mantini
, M. G.
Perrucci
, C.
Del Gratta
, G. L.
Romani
, and M.
Corbetta
, “Electrophysiological signatures of resting state networks in the human brain
,” Proc. Natl. Acad. Sci. U.S.A.
104
, 13170
–13175
(2007
). 23.
E.
Tagliazucchi
, F.
Von Wegner
, A.
Morzelewski
, V.
Brodbeck
, and H.
Laufs
, “Dynamic bold functional connectivity in humans and its electrophysiological correlates
,” Front. Hum. Neurosci.
6
, 339
(2012
). 24.
A.
Demertzi
, E.
Tagliazucchi
, S.
Dehaene
, G.
Deco
, P.
Barttfeld
, F.
Raimondo
, C.
Martial
, D.
Fernández-Espejo
, B.
Rohaut
, H.
Voss
et al., “Human consciousness is supported by dynamic complex patterns of brain signal coordination
,” Sci. Adv.
5
, eaat7603
(2019
). 25.
E.
Tagliazucchi
, F.
von Wegner
, A.
Morzelewski
, V.
Brodbeck
, K.
Jahnke
, and H.
Laufs
, “Breakdown of long-range temporal dependence in default mode and attention networks during deep sleep
,” Proc. Natl. Acad. Sci. U.S.A.
110
, 15419
–15424
(2013
). 26.
E.
Tagliazucchi
and H.
Laufs
, “Decoding wakefulness levels from typical fMRI resting-state data reveals reliable drifts between wakefulness and sleep
,” Neuron
82
, 695
–708
(2014
). 27.
P.
Barttfeld
, L.
Uhrig
, J. D.
Sitt
, M.
Sigman
, B.
Jarraya
, and S.
Dehaene
, “Signature of consciousness in the dynamics of resting-state brain activity
,” Proc. Natl. Acad. Sci. U.S.A.
112
, 887
–892
(2015
). 28.
M.
Greicius
, “Resting-state functional connectivity in neuropsychiatric disorders
,” Curr. Opin. Neurol.
21
, 424
–430
(2008
). 29.
A. T.
Drysdale
, L.
Grosenick
, J.
Downar
, K.
Dunlop
, F.
Mansouri
, Y.
Meng
, R. N.
Fetcho
, B.
Zebley
, D. J.
Oathes
, A.
Etkin
et al., “Resting-state connectivity biomarkers define neurophysiological subtypes of depression
,” Nat. Med.
23
, 28
–38
(2017
). 30.
M. F.
Glasser
, S. M.
Smith
, D. S.
Marcus
, J. L.
Andersson
, E. J.
Auerbach
, T. E.
Behrens
, T. S.
Coalson
, M. P.
Harms
, M.
Jenkinson
, S.
Moeller
et al., “The human connectome project’s neuroimaging approach
,” Nat. Neurosci.
19
, 1175
–1187
(2016
). 31.
P.
Sanz-Leon
, S. A.
Knock
, A.
Spiegler
, and V. K.
Jirsa
, “Mathematical framework for large-scale brain network modeling in the virtual brain
,” NeuroImage
111
, 385
–430
(2015
). 32.
M.
Breakspear
, “Dynamic models of large-scale brain activity
,” Nat. Neurosci.
20
, 340
–352
(2017
). 33.
A semi-empirical model combines simulated local dynamics with empirical estimates of anatomical and functional connectivity.
34.
G.
Deco
, J.
Cruzat
, J.
Cabral
, G. M.
Knudsen
, R. L.
Carhart-Harris
, P. C.
Whybrow
, N. K.
Logothetis
, and M. L.
Kringelbach
, “Whole-brain multimodal neuroimaging model using serotonin receptor maps explains non-linear functional effects of LSD
,” Curr. Biol.
28
, 3065
–3074
(2018
). 35.
V. K.
Jirsa
, T.
Proix
, D.
Perdikis
, M. M.
Woodman
, H.
Wang
, J.
Gonzalez-Martinez
, C.
Bernard
, C.
Bénar
, M.
Guye
, P.
Chauvel
et al., “The virtual epileptic patient: Individualized whole-brain models of epilepsy spread
,” NeuroImage
145
, 377
–388
(2017
). 36.
M. L.
Kringelbach
, J.
Cruzat
, J.
Cabral
, G. M.
Knudsen
, R.
Carhart-Harris
, P. C.
Whybrow
, N. K.
Logothetis
, and G.
Deco
, “Dynamic coupling of whole-brain neuronal and neurotransmitter systems
,” Proc. Natl. Acad. Sci. U.S.A.
117
, 9566
–9576
(2020
). 37.
G.
Deco
, J.
Cruzat
, J.
Cabral
, E.
Tagliazucchi
, H.
Laufs
, N. K.
Logothetis
, and M. L.
Kringelbach
, “Awakening: Predicting external stimulation to force transitions between different brain states
,” Proc. Natl. Acad. Sci. U.S.A.
116
, 18088
–18097
(2019
). 38.
G.
Deco
, J.
Cabral
, V. M.
Saenger
, M.
Boly
, E.
Tagliazucchi
, H.
Laufs
, E.
Van Someren
, B.
Jobst
, A.
Stevner
, and M. L.
Kringelbach
, “Perturbation of whole-brain dynamics in silico reveals mechanistic differences between brain states
,” NeuroImage
169
, 46
–56
(2018
). 39.
G.
Deco
, M. L.
Kringelbach
, V. K.
Jirsa
, and P.
Ritter
, “The dynamics of resting fluctuations in the brain: Metastability and its dynamical cortical core
,” Sci. Rep.
7
, 3095
(2017
). 40.
Y. S.
Perl
, C.
Pallacivini
, I. P.
Ipina
, M. L.
Kringelbach
, G.
Deco
, H.
Laufs
, and E.
Tagliazucchi
, “Data augmentation based on dynamical systems for the classification of brain states,” bioRxiv (2020).41.
Y. S.
Perl
, H.
Boccacio
, I.
Pérez-Ipiña
, F.
Zamberlán
, H.
Laufs
, M.
Kringelbach
, G.
Deco
, and E.
Tagliazucchi
, “Generative embeddings of brain collective dynamics using variational autoencoders,” arXiv:2007.01378 (2020).42.
Y. S.
Perl
, C.
Pallavicini
, I. P.
Ipina
, A.
Demertzi
, V.
Bonhomme
, C.
Martial
, R.
Panda
, J.
Annen
, A.
Ibanez
, M.
Kringelbach
et al., “Perturbations in dynamical models of whole-brain activity dissociate between the level and stability of consciousness,” bioRxiv (2020).43.
I. P.
Ipiña
, P. D.
Kehoe
, M.
Kringelbach
, H.
Laufs
, A.
Ibañez
, G.
Deco
, Y. S.
Perl
, and E.
Tagliazucchi
, “Modeling regional changes in dynamic stability during sleep and wakefulness
,” NeuroImage
215
, 116833
(2020
). 44.
B. M.
Jobst
, R.
Hindriks
, H.
Laufs
, E.
Tagliazucchi
, G.
Hahn
, A.
Ponce-Alvarez
, A. B.
Stevner
, M. L.
Kringelbach
, and G.
Deco
, “Increased stability and breakdown of brain effective connectivity during slow-wave sleep: Mechanistic insights from whole-brain computational modelling
,” Sci. Rep.
7
, 4634
(2017
). 45.
T.
Kunze
, A.
Hunold
, J.
Haueisen
, V.
Jirsa
, and A.
Spiegler
, “Transcranial direct current stimulation changes resting state functional connectivity: A large-scale brain network modeling study
,” NeuroImage
140
, 174
–187
(2016
). 46.
G.
Deco
, V. K.
Jirsa
, P. A.
Robinson
, M.
Breakspear
, and K.
Friston
, “The dynamic brain: From spiking neurons to neural masses and cortical fields
,” PLoS Comput. Biol.
4
, e1000092
(2008
). 47.
Phenomenological models are concerned with simple mechanisms that produce dynamics matching those observed in the experimental data. The differential equations and their parameters are not chosen to be biophysically realistic but instead to display certain desired qualitative behaviors seen in the data. However, the dynamics of realistic models can be locally reduced to phenomenological models by finding their normal form.
48.
M.
Golos
, V.
Jirsa
, and E.
Daucé
, “Multistability in large scale models of brain activity
,” PLoS Comput. Biol.
11
, e1004644
(2015
). 49.
E. C.
Hansen
, D.
Battaglia
, A.
Spiegler
, G.
Deco
, and V. K.
Jirsa
, “Functional connectivity dynamics: Modeling the switching behavior of the resting state
,” NeuroImage
105
, 525
–535
(2015
). 50.
S. M.
Smith
, D.
Vidaurre
, C. F.
Beckmann
, M. F.
Glasser
, M.
Jenkinson
, K. L.
Miller
, T. E.
Nichols
, E. C.
Robinson
, G.
Salimi-Khorshidi
, M. W.
Woolrich
et al., “Functional connectomics from resting-state fMRI
,” Trends Cogn. Sci.
17
, 666
–682
(2013
). 51.
S. H.
Strogatz
, Nonlinear Dynamics and Chaos with Student Solutions Manual: With Applications to Physics, Biology, Chemistry, and Engineering
(CRC Press
, 2018
).52.
A.
Palacios
, “Heteroclinic cycles
,” Scholarpedia
2
, 2352
(2007
). 53.
I.
Tsuda
, “Chaotic itinerancy
,” Scholarpedia J.
8
, 4459
(2013
). 54.
A.
Soong
and C.
Stuart
, “Evidence of chaotic dynamics underlying the human alpha-rhythm electroencephalogram
,” Biol. Cybern.
62
, 55
–62
(1989
). 55.
W. S.
Pritchard
and D. W.
Duke
, “Dimensional analysis of no-task human EEG using the Grassberger-Procaccia method
,” Psychophysiology
29
, 182
–192
(1992
). 56.
A.
Babloyantz
, J.
Salazar
, and C.
Nicolis
, “Evidence of chaotic dynamics of brain activity during the sleep cycle
,” Phys. Lett. A
111
, 152
–156
(1985
). 57.
A.
Babloyantz
and A.
Destexhe
, “Low-dimensional chaos in an instance of epilepsy
,” Proc. Natl. Acad. Sci. U.S.A.
83
, 3513
–3517
(1986
). 58.
C. A.
Skarda
and W. J.
Freeman
, “How brains make chaos in order to make sense of the world
,” Behav. Brain Sci.
10
, 161
–173
(1987
). 59.
H.
Korn
and P.
Faure
, “Is there chaos in the brain? II. Experimental evidence and related models
,” C. R. Biol.
326
, 787
–840
(2003
). 60.
P.
Faure
and H.
Korn
, “Is there chaos in the brain? I. Concepts of nonlinear dynamics and methods of investigation
,” C. R. Acad. Sci. Ser. III
324
, 773
–793
(2001
).61.
G. T.
Einevoll
, A.
Destexhe
, M.
Diesmann
, S.
Grün
, V.
Jirsa
, M.
de Kamps
, M.
Migliore
, T. V.
Ness
, H. E.
Plesser
, and F.
Schürmann
, “The scientific case for brain simulations
,” Neuron
102
, 735
–744
(2019
). 62.
C.
Letellier
and O. E.
Rossler
, “Rossler attractor
,” Scholarpedia
1
, 1721
(2006
). 63.
S.
Petkoski
and V. K.
Jirsa
, “Transmission time delays organize the brain network synchronization
,” Philos. Trans. R. Soc. A
377
, 20180132
(2019
). 64.
P.
Hagmann
, L.
Cammoun
, X.
Gigandet
, R.
Meuli
, C. J.
Honey
, V. J.
Wedeen
, and O.
Sporns
, “Mapping the structural core of human cerebral cortex
,” PLoS Biol.
6
, e159
(2008
). 65.
R. B.
Berry
, R.
Brooks
, C. E.
Gamaldo
, S. M.
Harding
, C.
Marcus
, B. V.
Vaughn
et al., The AASM Manual for the Scoring of Sleep and Associated Events: Rules, Terminology and Technical Specifications (American Academy of Sleep Medicine, Darien, IL, 2012), Vol. 176, p. 2012.66.
N.
Tzourio-Mazoyer
, B.
Landeau
, D.
Papathanassiou
, F.
Crivello
, O.
Etard
, N.
Delcroix
, B.
Mazoyer
, and M.
Joliot
, “Automated anatomical labeling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain
,” NeuroImage
15
, 273
–289
(2002
). 67.
G. H.
Glover
, T.-Q.
Li
, and D.
Ress
, “Image-based method for retrospective correction of physiological motion effects in fMRI: Retroicor
,” Magn. Reson. Med.
44
, 162
–167
(2000
). 68.
D.
Cordes
, V. M.
Haughton
, K.
Arfanakis
, J. D.
Carew
, P. A.
Turski
, C. H.
Moritz
, M. A.
Quigley
, and M. E.
Meyerand
, “Frequencies contributing to functional connectivity in the cerebral cortex in “resting-state” data
,” Am. J. Neuroradiol.
22
, 1326
–1333
(2001
).69.
R.
Dosselmann
and X. D.
Yang
, “A comprehensive assessment of the structural similarity index
,” Signal Image Video Process.
5
, 81
–91
(2011
). 70.
Z.
Wang
, A. C.
Bovik
, H. R.
Sheikh
, and E. P.
Simoncelli
, “Image quality assessment: From error visibility to structural similarity
,” IEEE Trans. Image Process.
13
, 600
–612
(2004
). 71.
A.
Pikovsky
, J.
Kurths
, M.
Rosenblum
, and J.
Kurths
, Synchronization: A Universal Concept in Nonlinear Sciences
(Cambridge University Press
, 2003
), Vol. 12.72.
J. C.
Sprott
, Chaos and Time-Series Analysis
(Oxford University Press
, 2003
), Vol. 69.73.
K.
Xu
, J. P.
Maidana
, S.
Castro
, and P.
Orio
, “Synchronization transition in neuronal networks composed of chaotic or non-chaotic oscillators
,” Sci. Rep.
8
, 1
(2018
). 74.
C. O.
Fritz
, P. E.
Morris
, and J. J.
Richler
, “Effect size estimates: Current use, calculations, and interpretation
,” J. Exp. Psychol. Gen.
141
, 2
(2012
). 75.
D.
Kleppner
and R.
Kolenkow
, An Introduction to Mechanics
(Cambridge University Press
, 2014
).76.
L.
Abbott
and T. B.
Kepler
, “Model neurons: From Hodgkin-Huxley to Hopfield,” in Statistical Mechanics of Neural Networks (Springer, 1990), pp. 5–18.77.
S. W.
Oh
, J. A.
Harris
, L.
Ng
, B.
Winslow
, N.
Cain
, S.
Mihalas
, Q.
Wang
, C.
Lau
, L.
Kuan
, A. M.
Henry
et al., “A mesoscale connectome of the mouse brain
,” Nature
508
, 207
–214
(2014
). 78.
H.
Markram
, “The human brain project
,” Sci. Am.
306
, 50
–55
(2012
). 79.
J.
Courtiol
, M.
Guye
, F.
Bartolomei
, S.
Petkoski
, and V. K.
Jirsa
, “Dynamical mechanisms of interictal resting-state functional connectivity in epilepsy
,” J. Neurosci.
40
, 5572
–5588
(2020
).80.
M.
Schirner
, A. R.
McIntosh
, V.
Jirsa
, G.
Deco
, and P.
Ritter
, “Inferring multi-scale neural mechanisms with brain network modelling
,” Elife
7
, e28927
(2018
). 81.
E. T.
Rolls
and G.
Deco
, The Noisy Brain: Stochastic Dynamics as a Principle of Brain Function
(Oxford University Press
, Oxford
, 2010
), Vol. 34.82.
R. M.
Hutchison
, T.
Womelsdorf
, E. A.
Allen
, P. A.
Bandettini
, V. D.
Calhoun
, M.
Corbetta
, S.
Della Penna
, J. H.
Duyn
, G. H.
Glover
, J.
Gonzalez-Castillo
et al., “Dynamic functional connectivity: Promise, issues, and interpretations
,” NeuroImage
80
, 360
–378
(2013
). 83.
A. A.
Faisal
, L. P.
Selen
, and D. M.
Wolpert
, “Noise in the nervous system
,” Nat. Rev. Neurosci.
9
, 292
–303
(2008
). 84.
A.
Blumer
, A.
Ehrenfeucht
, D.
Haussler
, and M. K.
Warmuth
, “Occam’s razor
,” Inf. Process. Lett.
24
, 377
–380
(1987
). 85.
P. E.
Rapp
, “Is there evidence for chaos in the human central nervous system
,” in Chaos Theory in Psychology and the Life Sciences
, edited by R. Robertson and A. Combs (Psychology Press, 2014
).86.
H.
Preissl
, W.
Lutzenberger
, and F.
Pulvermüller
, “Is there chaos in the brain?
,” Behav. Brain Sci.
19
, 307
–308
(1996
). 87.
D.
Hansel
and H.
Sompolinsky
, “Synchronization and computation in a chaotic neural network
,” Phys. Rev. Lett.
68
, 718
(1992
). 88.
M.
Rabinovich
and H.
Abarbanel
, “The role of chaos in neural systems
,” Neuroscience
87
, 5
–14
(1998
). 89.
J. L.
Hindmarsh
and R.
Rose
, “A model of neuronal bursting using three coupled first order differential equations
,” Proc. R. Soc. Lond. B. Biol. Sci.
221
, 87
–102
(1984
). 90.
D.
Hansel
and H.
Sompolinsky
, “Chaos and synchrony in a model of a hypercolumn in visual cortex
,” J. Comput. Neurosci.
3
, 7
–34
(1996
). 91.
D.
Battaglia
, N.
Brunel
, and D.
Hansel
, “Temporal decorrelation of collective oscillations in neural networks with local inhibition and long-range excitation
,” Phys. Rev. Lett.
99
, 238106
(2007
). 92.
J.
Kadmon
and H.
Sompolinsky
, “Transition to chaos in random neuronal networks
,” Phys. Rev. X
5
, 041030
(2015
). 93.
P.
Orio
, M.
Gatica
, R.
Herzog
, J. P.
Maidana
, S.
Castro
, and K.
Xu
, “Chaos versus noise as drivers of multistability in neural networks
,” Chaos
28
, 106321
(2018
). 94.
G.
Deco
, V.
Jirsa
, A. R.
McIntosh
, O.
Sporns
, and R.
Kötter
, “Key role of coupling, delay, and noise in resting brain fluctuations
,” Proc. Natl. Acad. Sci. U.S.A.
106
, 10302
–10307
(2009
). 95.
S.
Petkoski
, J. M.
Palva
, and V. K.
Jirsa
, “Phase-lags in large scale brain synchronization: Methodological considerations and in-silico analysis
,” PLoS Comput. Biol.
14
, e1006160
(2018
). 96.
J.
Cabral
, H.
Luckhoo
, M.
Woolrich
, M.
Joensson
, H.
Mohseni
, A.
Baker
, M. L.
Kringelbach
, and G.
Deco
, “Exploring mechanisms of spontaneous functional connectivity in MEG: How delayed network interactions lead to structured amplitude envelopes of band-pass filtered oscillations
,” NeuroImage
90
, 423
–435
(2014
). 97.
T.
Bayne
and J.
Hohwy
, “Modes of consciousness,” in Finding Consciousness: Neuroscience, Ethics and Law of Severe Brain Damage (Oxford University Press, 2016), pp. 57–80.98.
J.
Piccinini
, “Awake time series
,” figshare dataset
(2020
), see .© 2021 Author(s).
2021
Author(s)
You do not currently have access to this content.
