54
B. Pietras and A. Daffertshofer
65. S. Petkoski, V.K. Jirsa, Transmission time delays organize the brain network synchronization.
Philos. Trans. R. Soc. A 377(2153), 20180132 (2019)
66. S. Petkoski, J.M. Palva, V.K. Jirsa, Phase-lags in large scale brain synchronization: methodological considerations and in-silico analysis. PLoS Comput. Biol. 14(7), e1006160 (2018)
67. B. Pietras, A. Daffertshofer, Network dynamics of coupled oscillators and phase reduction
techniques. Phys. Rep. 819, 1 (2019)
68. M.A. Porter, J.P. Gleeson, Dynamical systems on networks. Front. Appl. Dyn. Syst.: Rev. Tutor.
4, (2016)
69. J.G. Restrepo, E. Ott, B.R. Hunt, Synchronization in large directed networks of coupled phase
oscillators. Chaos 16(1), 015107 (2006). https://doi.org/10.1063/1.2148388
70. F.A. Rodrigues, T.K.D. Peron, P. Ji, J. Kurths, The Kuramoto model in complex networks.
Phys. Rep. 610, 1 (2016)
71. A. Rothkegel, K. Lehnertz, Recurrent events of synchrony in complex networks of pulsecoupled oscillators. Europhys. Lett. 95(3), 38001 (2011)
72. A. Rothkegel, K. Lehnertz, Irregular macroscopic dynamics due to chimera states in smallworld networks of pulse-coupled oscillators. New J. Phys. 16(5), 055006 (2014)
73. P. Sanz-Leon, S.A. Knock, A. Spiegler, V.K. Jirsa, Mathematical framework for large-scale
brain network modeling in the virtual brain. NeuroImage 111, 385 (2015)
74. P. Sauseng, W. Klimesch, What does phase information of oscillatory brain activity tell us
about cognitive processes? Neurosci. Biobehav. Rev. 32(5), 1001 (2008)
75. B. Schack, S. Weiss, Quantification of phase synchronization phenomena and their importance
for verbal memory processes. Biol. Cybern. 92(4), 275 (2005)
76. H. Schuster, P. Wagner, A model for neuronal oscillations in the visual cortex. Biol. Cybern.
64(1), 77 (1990)
77. M.A. Schwemmer, T.J. Lewis, The Theory of Weakly Coupled Oscillators, in Phase Response
Curves in Neuroscience: Theory, Experiment, and Analysis, ed. by N.W. Schultheiss, A.A.
Prinz, R.J. Butera (Springer Science & Business Media, New York, NY, 2012), pp. 3–31
78. S. Shirasaka, W. Kurebayashi, H. Nakao, Phase-amplitude reduction of transient dynamics far
from attractors for limit-cycling systems. Chaos 27(2), 023119 (2017)
79. S. Smale, A Mathematical Model of Two Cells Via Turing’s Equation, in The Hopf Bifurcation
and Its Applications (Springer, New York, 1976), pp. 354–367
80. M. Steriade, Cellular substrates of brain rhythms, in Electroencephalography Basic Principles,
Clinical Applications, and Related Fields, ed. by E. Niedermeyer, F. Lopes Da Silva (Lippincott
Williams & Wilkins, Philadelphia, 2005), pp. 31–84
81. S.H. Strogatz, Exploring complex networks. Nature 410(6825), 268 (2001)
82. G. Thut, C. Miniussi, J. Gross, The functional importance of rhythmic activity in the brain.
Curr. Biol. 22(16), R658 (2012)
83. R. Ton, G. Deco, A. Daffertshofer, Structure-function discrepancy: inhomogeneity and delays
in synchronized neural networks. PLoS Comput. Biol. 10(7), e1003736 (2014)
84. F. Varela, J.P. Lachaux, E. Rodriguez, J. Martinerie, The brainweb: phase synchronization and
large-scale integration. Nat. Rev. Neurosci. 2(4), 229 (2001)
85. X.F. Wang, G. Chen, Synchronization in small-world dynamical networks. Int. J. Bifurc. Chaos
12(01), 187 (2002)
86. D.J. Watts, S.H. Strogatz, Collective dynamics of ‘small-world’ networks. Nature 393(6684),
440 (1998)
87. K.C. Wedgwood, K.K. Lin, R. Thul, S. Coombes, Phase-amplitude descriptions of neural
oscillator models. J. Math. Neurosci. 3(1), 2 (2013)
88. H.R. Wilson, J.D. Cowan, Excitatory and inhibitory interactions in localized populations of
model neurons. Biophys. J. 12(1), 1 (1972)
89. D. Wilson, B. Ermentrout, Greater accuracy and broadened applicability of phase reduction
using isostable coordinates. J. Math. Biol. (2017)
B. Pietras and A. Daffertshofer
65. S. Petkoski, V.K. Jirsa, Transmission time delays organize the brain network synchronization.
Philos. Trans. R. Soc. A 377(2153), 20180132 (2019)
66. S. Petkoski, J.M. Palva, V.K. Jirsa, Phase-lags in large scale brain synchronization: methodological considerations and in-silico analysis. PLoS Comput. Biol. 14(7), e1006160 (2018)
67. B. Pietras, A. Daffertshofer, Network dynamics of coupled oscillators and phase reduction
techniques. Phys. Rep. 819, 1 (2019)
68. M.A. Porter, J.P. Gleeson, Dynamical systems on networks. Front. Appl. Dyn. Syst.: Rev. Tutor.
4, (2016)
69. J.G. Restrepo, E. Ott, B.R. Hunt, Synchronization in large directed networks of coupled phase
oscillators. Chaos 16(1), 015107 (2006). https://doi.org/10.1063/1.2148388
70. F.A. Rodrigues, T.K.D. Peron, P. Ji, J. Kurths, The Kuramoto model in complex networks.
Phys. Rep. 610, 1 (2016)
71. A. Rothkegel, K. Lehnertz, Recurrent events of synchrony in complex networks of pulsecoupled oscillators. Europhys. Lett. 95(3), 38001 (2011)
72. A. Rothkegel, K. Lehnertz, Irregular macroscopic dynamics due to chimera states in smallworld networks of pulse-coupled oscillators. New J. Phys. 16(5), 055006 (2014)
73. P. Sanz-Leon, S.A. Knock, A. Spiegler, V.K. Jirsa, Mathematical framework for large-scale
brain network modeling in the virtual brain. NeuroImage 111, 385 (2015)
74. P. Sauseng, W. Klimesch, What does phase information of oscillatory brain activity tell us
about cognitive processes? Neurosci. Biobehav. Rev. 32(5), 1001 (2008)
75. B. Schack, S. Weiss, Quantification of phase synchronization phenomena and their importance
for verbal memory processes. Biol. Cybern. 92(4), 275 (2005)
76. H. Schuster, P. Wagner, A model for neuronal oscillations in the visual cortex. Biol. Cybern.
64(1), 77 (1990)
77. M.A. Schwemmer, T.J. Lewis, The Theory of Weakly Coupled Oscillators, in Phase Response
Curves in Neuroscience: Theory, Experiment, and Analysis, ed. by N.W. Schultheiss, A.A.
Prinz, R.J. Butera (Springer Science & Business Media, New York, NY, 2012), pp. 3–31
78. S. Shirasaka, W. Kurebayashi, H. Nakao, Phase-amplitude reduction of transient dynamics far
from attractors for limit-cycling systems. Chaos 27(2), 023119 (2017)
79. S. Smale, A Mathematical Model of Two Cells Via Turing’s Equation, in The Hopf Bifurcation
and Its Applications (Springer, New York, 1976), pp. 354–367
80. M. Steriade, Cellular substrates of brain rhythms, in Electroencephalography Basic Principles,
Clinical Applications, and Related Fields, ed. by E. Niedermeyer, F. Lopes Da Silva (Lippincott
Williams & Wilkins, Philadelphia, 2005), pp. 31–84
81. S.H. Strogatz, Exploring complex networks. Nature 410(6825), 268 (2001)
82. G. Thut, C. Miniussi, J. Gross, The functional importance of rhythmic activity in the brain.
Curr. Biol. 22(16), R658 (2012)
83. R. Ton, G. Deco, A. Daffertshofer, Structure-function discrepancy: inhomogeneity and delays
in synchronized neural networks. PLoS Comput. Biol. 10(7), e1003736 (2014)
84. F. Varela, J.P. Lachaux, E. Rodriguez, J. Martinerie, The brainweb: phase synchronization and
large-scale integration. Nat. Rev. Neurosci. 2(4), 229 (2001)
85. X.F. Wang, G. Chen, Synchronization in small-world dynamical networks. Int. J. Bifurc. Chaos
12(01), 187 (2002)
86. D.J. Watts, S.H. Strogatz, Collective dynamics of ‘small-world’ networks. Nature 393(6684),
440 (1998)
87. K.C. Wedgwood, K.K. Lin, R. Thul, S. Coombes, Phase-amplitude descriptions of neural
oscillator models. J. Math. Neurosci. 3(1), 2 (2013)
88. H.R. Wilson, J.D. Cowan, Excitatory and inhibitory interactions in localized populations of
model neurons. Biophys. J. 12(1), 1 (1972)
89. D. Wilson, B. Ermentrout, Greater accuracy and broadened applicability of phase reduction
using isostable coordinates. J. Math. Biol. (2017)