Synchronization in Functional Networks of the Human Brain

  • Philipp HövelEmail author
  • Aline Viol
  • Philipp Loske
  • Leon Merfort
  • Vesna Vuksanović


Understanding the relationship between structural and functional organization represents one of the most important challenges in neuroscience. An increasing amount of studies show that this organization can be better understood by considering the brain as an interactive complex network. This approach has inspired a large number of computational models that combine experimental data with numerical simulations of brain interactions. In this paper, we present a summary of a data-driven computational model of synchronization between distant cortical areas that share a large number of overlapping neighboring (anatomical) connections. Such connections are derived from in vivo measures of brain connectivity using diffusion-weighted magnetic resonance imaging and are additionally informed by the presence of significant resting-state functionally correlated links between the areas involved. The dynamical processes of brain regions are simulated by a combination of coupled oscillator systems and a hemodynamic response model. The coupled oscillatory systems are represented by the Kuramoto phase oscillators, thus modeling phase synchrony between regional activities. The focus of this modeling approach is to characterize topological properties of functional brain correlation related to synchronization of the regional neural activity. The proposed model is able to reproduce remote synchronization between brain regions reaching reasonable agreement with the experimental functional connectivities. We show that the best agreement between model and experimental data is reached for dynamical states that exhibit a balance of synchrony and variations in synchrony providing the integration of activity between distant brain regions.


Nonlinear dynamics Synchronization Brain connectivity Kuramoto phase oscillator Neural activity 

Mathematics Subject Classification

92B25 34C15 92C42 



AV and PH acknowledge support by Deutsche Forschungsgemeinschaft under Grant No. HO4695/3-1 and within the framework of Collaborative Research Center 910. We thank Yasser Iturria-Medina for sharing the DW-MRI data including fiber lengths used in the study. We also thank Jason Bassett for helpful discussions.


  1. Acebrón, J.A., Bonilla, L.L., Pérez Vicente, C.J., Ritort, F., Spigler, R.: The Kuramoto model: a simple paradigm for synchronization phenomena. Rev. Mod. Phys. 77, 137 (2005)CrossRefGoogle Scholar
  2. Arenas, A., Díaz-Guilera, A., Pérez Vicente, C.J.: Synchronization reveals topological scales in complex networks. Phys. Rev. Lett. 96, 114102 (2006)CrossRefGoogle Scholar
  3. Balanov, A.G., Janson, N.B., Postnov, D.E., Sosnovtseva, O.V.: Synchronization: From Simple to Complex. Springer, Berlin (2009)zbMATHGoogle Scholar
  4. Barttfeld, P., Uhrig, L., Sitt, J.D., Sigman, M., Jarraya, B., Dehaene, S.: Signature of consciousness in the dynamics of resting-state brain activity. Proc. Natl. Acad. Sci. USA 112, 887 (2015)CrossRefGoogle Scholar
  5. Bergner, A., Frasca, M., Sciuto, G., Buscarino, A., Ngamga, E.J., Fortuna, L., Kurths, J.: Remote synchronization in star networks. Phys. Rev. E 85, 026208 (2012)CrossRefGoogle Scholar
  6. Biswal, B.B.: Toward discovery science of human brain function. Proc. Natl. Acad. Sci. USA 107, 4734 (2010)CrossRefGoogle Scholar
  7. Biswal, B., Yetkin, F.Z., Haughton, V.M., Hyde, J.S.: Functional connectivity in the motor cortex of resting human brain using echo-planar MRI. Magn. Reson. Med. 34, 537 (1995)CrossRefGoogle Scholar
  8. Boccaletti, S., Kurths, J., Osipov, G., Valladares, D.L., Zhou, C.S.: The synchronization of chaotic systems. Phys. Rep. 366, 1 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  9. Bola, M., Sabel, B.A.: Dynamic reorganization of brain functional networks during cognition. NeuroImage 114, 398 (2015)CrossRefGoogle Scholar
  10. Breakspear, M., Roberts, J.A., Terry, J.R., Rodrigues, S., Mahant, N., Robinson, P.A.: A unifying explanation of primary generalized seizures through nonlinear brain modeling and bifurcation analysis. Cereb. Cortex 16, 1296 (2006)CrossRefGoogle Scholar
  11. Breakspear, M., Heitmann, S., Daffertshofer, A.: Generative models of cortical oscillations: neurobiological implications of the Kuramoto model. Front. Hum. Neurosci. 4, 190 (2010)CrossRefGoogle Scholar
  12. Bressler, S.L., Menon, V.: Large-scale brain networks in cognition: emerging methods and principles. Trends Cogn. Sci. 14, 277 (2010)CrossRefGoogle Scholar
  13. Bullmore, E.T., Bassett, D.S.: Brain graphs: graphical models of the human brain connectome. Annu. Rev. Clin. Psychol. 7, 113 (2011)CrossRefGoogle Scholar
  14. Bullmore, E.T., Sporns, O.: Complex brain networks: graph theoretical analysis of structural and functional systems. Nat. Rev. Neurosci. 10, 186 (2009)CrossRefGoogle Scholar
  15. Cabral, J., Hugues, E., Sporns, O., Deco, G.: Role of local network oscillations in resting-state functional connectivity. Neuroimage 57, 130 (2011)CrossRefGoogle Scholar
  16. Cabral, J., Hugues, E., Kringelbach, M.L., Deco, G.: Modeling the outcome of structural disconnection on resting-state functional connectivity. Neuroimage 62, 1342 (2012)CrossRefGoogle Scholar
  17. Cabral, J., Fernandes, H.M., Van Hartevelt, T.J., James, A.C., Kringelbach, M.L.: Structural connectivity in schizophrenia and its impact on the dynamics of spontaneous functional networks. Chaos 23, 046111 (2013)MathSciNetCrossRefGoogle Scholar
  18. Cabral, J., Luckhoo, H., Woolrich, M.W., Joensson, M., Mohseni, H., Baker, A., Kringelbach, M.L., Deco, G.: 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 (2014a)CrossRefGoogle Scholar
  19. Cabral, J., Kringelbach, M.L., Deco, G.: Exploring the network dynamics underlying brain activity during rest. Prog. Neurobiol. 114, 102 (2014b)CrossRefGoogle Scholar
  20. Carhart-Harris, R., Muthukumaraswamy, S., Roseman, L., Kaelen, M., Droog, W., Murphy, K., Tagliazucchi, E., Schenberg, E.E., Nest, T., Orban, C., Leech, R., Williams, L.T., Williams, T.M., Bolstridge, M., Sessa, B., McGonigle, J., Sereno, M.I., Nichols, D., Hellyer, P.J., Hobden, P., Evans, J., Singh, K.D., Wise, R.G., Curran, H.V., Feilding, A., Nutt, D.J.: Neural correlates of the LSD experience revealed by multimodal neuroimaging. Proc. Natl. Acad. Sci. USA 113, 4853 (2016)CrossRefGoogle Scholar
  21. Ciccarelli, O., Catani, M., Johansen-Berg, H., Clark, C., Thompson, A.: Diffusion-based tractography in neurological disorders: concepts, applications, and future developments. Lancet Neurol. 7, 715 (2008)CrossRefGoogle Scholar
  22. Clayden, J.D.: Imaging connectivity: MRI and the structural networks of the brain. Funct. Neurol. 28, 197 (2013)Google Scholar
  23. Cole, D.M., Smith, S.M., Beckmann, C.F.: Advances and pitfalls in the analysis and interpretation of resting-state FMRI data. Front. Syst. Neurosci. 4, 8 (2010)Google Scholar
  24. Damoiseaux, J.S., Rombouts, S.A.R.B., Barkhof, F., Scheltens, P., Stam, C.J., Smith, S.M., Beckmann, C.F.: Consistent resting-state networks across healthy subjects. Proc. Natl. Acad. Sci. USA 103, 13848 (2006)CrossRefGoogle Scholar
  25. Dang-Vu, T.T., Schabus, M., Desseilles, M., Albouy, G., Boly, M., Darsaud, A., Gais, S., Rauchs, G., Sterpenich, V., Vandewalle, G., Carrier, J., Moonen, G., Balteau, E., Degueldre, C., Luxen, A., Phillips, C., Maquet, P.: Spontaneous neural activity during human slow wave sleep. Proc. Natl. Acad. Sci. USA 105, 15160 (2008)CrossRefGoogle Scholar
  26. Deco, G., Jirsa, V.K.: Ongoing cortical activity at rest: criticality, multistability, and ghost attractors. J. Neurosci. 32, 3366 (2012)CrossRefGoogle Scholar
  27. Deco, G., Kringelbach, M.L.: Great expectations: using whole-brain computational connectomics for understanding neuropsychiatric disorders. Neuron 84, 892 (2014)CrossRefGoogle Scholar
  28. Deco, G., Jirsa, V.K., McIntosh, A.R.: Emerging concepts for the dynamical organization of resting-state activity in the brain. Nat. Rev. Neurosci. 12, 43 (2011)CrossRefGoogle Scholar
  29. Deco, G., Jirsa, V.K., McIntosh, A.R.: Resting brains never rest: computational insights into potential cognitive architectures. Trends Neurosci. 36, 268 (2013)CrossRefGoogle Scholar
  30. Demirtas, M., Deco, G.: Chapter 4—computational models of dysconnectivity in large-scale resting-state networks. In: Anticevic, A., Murray, J.D. (eds.) Computational Psychiatry, pp. 87–116. Academic Press, New York (2018)CrossRefGoogle Scholar
  31. Desjardins, A.E., Kiehl, K.A., Liddle, P.F.: Removal of confounding effects of global signal in functional MRI analyses. NeuroImage 13, 751 (2001)CrossRefGoogle Scholar
  32. Farooq, H., Xu, J., Nam, J.W., Keefe, D.F., Yacoub, E., Georgiou, T., Lenglet, C.: Microstructure imaging of crossing (MIX) white matter fibers from diffusion MRI. Sci. Rep. 6, 38927 (2016)CrossRefGoogle Scholar
  33. Felleman, D.J., Van Essen, D.C.: Distributed hierarchical processing in the primate cerebral cortex. Cereb. Cortex 1, 1 (1991)CrossRefGoogle Scholar
  34. FitzHugh, R.: Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1, 445 (1961)CrossRefGoogle Scholar
  35. Friston, K., Dolan, R.J.: Computational and dynamic models in neuroimaging. NeuroImage 52, 752 (2010)CrossRefGoogle Scholar
  36. Friston, K., Mechelli, A., Turner, R., Price, C.J.: Nonlinear responses in fMRI: the balloon model, Volterra kernels, and other hemodynamics. NeuroImage 12, 466 (2000)CrossRefGoogle Scholar
  37. Greve, D.N., Brown, G.G., Mueller, B.A., Glover, G., Liu, T.T.: A survey of the sources of noise in fMRI. Psychometrika 78, 396 (2013)MathSciNetzbMATHCrossRefGoogle Scholar
  38. Hauptmann, C., Omel’chenko, O.E., Popovych, O., Maistrenko, Y., Tass, P.: Control of spatially patterned synchrony with multisite delayed feedback. Phys. Rev. E 76, 066209 (2007)MathSciNetCrossRefGoogle Scholar
  39. Haynes, J.D., Rees, G.: Decoding mental states from brain activity in humans. Nat. Rev. Neurosci. 7, 523 (2006)CrossRefGoogle Scholar
  40. Heeger, D.J., Ress, D.: What does MRI tell us about neuronal activity? Nat. Rev. Neurosci. 3, 142 (2002)CrossRefGoogle Scholar
  41. Hellyer, P.J., Shanahan, M., Scott, G., Wise, R.J.S., Sharp, D.J., Leech, R.: The control of global brain dynamics: opposing actions of frontoparietal control and default mode networks on attention. J. Neurosci. 34, 451 (2014)CrossRefGoogle Scholar
  42. Hodgkin, A.L., Huxley, A.F.: A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117, 500 (1952)CrossRefGoogle Scholar
  43. Honey, C.J., Sporns, O., Cammoun, L., Gigandet, X., Thiran, J.P., Meuli, R., Hagmann, P.: Predicting human resting-state functional connectivity from structural connectivity. Proc. Natl. Acad. Sci. USA 106, 2035 (2009)CrossRefGoogle Scholar
  44. Huang, Z., Dai, R., Wu, X., Yang, Z., Liu, D., Hu, J., Gao, L., Tang, W., Mao, Y., Jin, Y., Wu, X., Liu, B., Zhang, Y., Lu, L., Laureys, S., Weng, X., Northoff, G.: The self and its resting state in consciousness: an investigation of the vegetative state. Hum. Brain Mapp. 35, 1997 (2014)CrossRefGoogle Scholar
  45. Hutchings, F., Han, C.E., Keller, S.S., Weber, B., Taylor, P.N., Kaiser, M.: Predicting surgery targets in temporal lobe epilepsy through structural connectome based simulations. PLoS Comput. Biol. 11, e1004642 (2015)CrossRefGoogle Scholar
  46. Iturria-Medina, Y., Sotero, R.C., Canales-Rodríguez, E.J., Alemán-Gómez, Y., Melie-García, L.: Studying the human brain anatomical network via diffusion-weighted MRI and graph theory. NeuroImage 40, 1064 (2008)CrossRefGoogle Scholar
  47. Izhikevich, E.M.: Which model to use for cortical spiking neurons? IEEE Trans. Neural Netw. 15, 1063 (2004)CrossRefGoogle Scholar
  48. Jbabdi, S., Sotiropoulos, S.N., Haber, S.N., Van Essen, D.C., Behrens, T.E.: Measuring macroscopic brain connections in vivo. Nat. Neurosci. 18, 1546 (2015)CrossRefGoogle Scholar
  49. Jirsa, V.K., Haken, H.: Field theory of electromagnetic brain activity. Phys. Rev. Lett. 77, 960 (1996)CrossRefGoogle Scholar
  50. Kanwisher, N.: Functional specificity in the human brain: a window into the functional architecture of the mind. Proc. Natl. Acad. Sci. USA 107, 11163 (2010)CrossRefGoogle Scholar
  51. Keane, A., Dahms, T., Lehnert, J., Suryanarayana, S.A., Hövel, P., Schöll, E.: Synchronisation in networks of delay-coupled type-I excitable systems. Eur. Phys. J. B 85, 407 (2012)CrossRefGoogle Scholar
  52. Koch, M.A., Norris, D.G., Hund-Georgiadis, M.: An investigation of functional and anatomical connectivity using magnetic resonance imaging. NeuroImage 16, 241 (2002)CrossRefGoogle Scholar
  53. Kruggel, F., von Cramon, D.Y., Descombes, X.: Comparison of filtering methods for fMRI datasets. NeuroImage 10, 530 (1999)CrossRefGoogle Scholar
  54. Kuramoto, Y.: Self-entrainment of a population of coupled non-linear oscillators. In: Araki, H. (ed.) International Symposium on Mathematical Problems in Theoretical Physics, vol. 39 of Lecture Notes in Physics, pp. 420–422. Springer, Berlin (1975)CrossRefGoogle Scholar
  55. Lehnert, J., Dahms, T., Hövel, P., Schöll, E.: Loss of synchronization in complex neural networks with delay. Europhys. Lett. 96, 60013 (2011)CrossRefGoogle Scholar
  56. Liang, X., Tang, M., Dhamala, M., Liu, Z.: Phase synchronization of inhibitory bursting neurons induced by distributed time delays in chemical coupling. Phys. Rev. E 80, 066202 (2009)CrossRefGoogle Scholar
  57. Liu, Y., Liang, M., Zhou, Y., He, Y., Hao, Y., Song, M., Yu, C., Liu, H., Liu, Z., Jiang, T.: Disrupted small-world networks in schizophrenia. Brain 131, 945 (2008)CrossRefGoogle Scholar
  58. Lowe, M.J.: A historical perspective on the evolution of resting-state functional connectivity with MRI. Magn. Reson. Mater. Phys. 23, 279 (2010)CrossRefGoogle Scholar
  59. Masoller, C., Torrent, M.C., García-Ojalvo, J.: Interplay of subthreshold activity, time-delayed feedback, and noise on neuronal firing patterns. Phys. Rev. E 78, 041907 (2008)CrossRefGoogle Scholar
  60. Masoller, C., Torrent, M.C., García-Ojalvo, J.: Dynamics of globally delay-coupled neurons displaying subthreshold oscillations. Phil. Trans. R. Soc. A Math. Phys. Eng. Sci. 367, 3255 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  61. Mosekilde, E., Maistrenko, Y., Postnov, D.: Chaotic Synchronization: Applications to Living Systems. World Scientific, Singapore (2002)zbMATHCrossRefGoogle Scholar
  62. Muldoon, S.F., Pasqualetti, F., Gu, S., Cieslak, M., Grafton, S.T., Vettel, J.M., Bassett, D.S.: Stimulation-based control of dynamic brain networks. PLoS Comput. Biol. 12, e1005076 (2016)CrossRefGoogle Scholar
  63. Nagumo, J., Arimoto, S., Yoshizawa, S.: An active pulse transmission line simulating nerve axon. Proc. IRE 50, 2061 (1962)CrossRefGoogle Scholar
  64. Nicosia, V., Valencia, M., Chavez, M., Díaz-Guilera, A., Latora, V.: Remote synchronization reveals network symmetries and functional modules. Phys. Rev. Lett. 110, 174102 (2013)CrossRefGoogle Scholar
  65. Noirhomme, Q., Soddu, A., Lehembre, R., Vanhaudenhuyse, A., Boveroux, P., Boly, M., Laureys, S.: Brain connectivity in pathological and pharmacological coma. Front. Syst. Neurosci. 4, 160 (2010)CrossRefGoogle Scholar
  66. Onias, H., Viol, A., Palhano-Fontes, F., Andrade, K.C., Sturzbecher, M., Viswanathan, G.M., de Araujo, D.B.: Brain complex network analysis by means of resting state fMRI and graph analysis: will it be helpful in clinical epilepsy? Epilepsy Behav. 38, 71 (2014)CrossRefGoogle Scholar
  67. Pikovsky, A., Rosenblum, M.G., Kurths, J.: Synchronization: A Universal Concept in Nonlinear Sciences. Cambridge University Press, Cambridge (2001)zbMATHCrossRefGoogle Scholar
  68. Popovych, O., Yanchuk, S., Tass, P.: Delay- and coupling-induced firing patterns in oscillatory neural loops. Phys. Rev. Lett. 107, 228102 (2011)CrossRefGoogle Scholar
  69. Power, J.D., Mitra, A., Laumann, T.O., Snyder, A.Z., Schlaggar, B.L., Petersen, S.E.: Methods to detect, characterize, and remove motion artifact in resting state fMRI. Neuroimage 84, 320 (2014)CrossRefGoogle Scholar
  70. Rodrigues, F.A., Peron, T.K.D.M., Ji, P., Kurths, J.: The Kuramoto model in complex networks. Phys. Rep. 610, 1 (2016)MathSciNetzbMATHCrossRefGoogle Scholar
  71. Rossoni, E., Chen, Y., Ding, M., Feng, J.: Stability of synchronous oscillations in a system of Hodgkin–Huxley neurons with delayed diffusive and pulsed coupling. Phys. Rev. E 71, 061904 (2005)MathSciNetCrossRefGoogle Scholar
  72. Rubinov, M., Sporns, O.: Complex network measures of brain connectivity: uses and interpretations. Neuroimage 52, 1059 (2010)CrossRefGoogle Scholar
  73. Rubinov, M., Knock, S.A., Stam, C.J., Micheloyannis, S., Harris, A.W.F., Williams, L.M., Breakspear, M.: Small-world properties of nonlinear brain activity in schizophrenia. Hum. Brain Mapp. 30, 403 (2009)CrossRefGoogle Scholar
  74. Rudie, J.D., Brown, J.A., Beck-Pancer, D., Hernandez, L.M., Dennis, E.L., Thompson, P.M., Bookheimer, S.Y., Dapretto, M.: Altered functional and structural brain network organization in autism. NeuroImage Clin. 2, 79 (2013)CrossRefGoogle Scholar
  75. Sanz-Leon, P., Knock, S.A., Spiegler, A., Jirsa, V.K.: Mathematical framework for large-scale brain network modeling in The Virtual Brain. Neuroimage 111, 385 (2015)CrossRefGoogle Scholar
  76. Schall, J.D.: On building a bridge between brain and behavior. Annu. Rev. Psychol. 55, 23 (2004)CrossRefGoogle Scholar
  77. Schrouff, J., Perlbarg, V., Boly, M., Marrelec, G., Boveroux, P., Vanhaudenhuyse, A., Bruno, M.A., Laureys, S., Phillips, C., Pélégrini-Issac, M., Maquet, P., Benali, H.: Brain functional integration decreases during propofol-induced loss of consciousness. NeuroImage 57, 198 (2011)CrossRefGoogle Scholar
  78. Senthilkumar, D.V., Kurths, J., Lakshmanan, M.: Inverse synchronizations in coupled time-delay systems with inhibitory coupling. Chaos 19, 023107 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  79. Seth, A.K., Chorley, P., Barnett, L.C.: Granger causality analysis of fMRI BOLD signals is invariant to hemodynamic convolution but not downsampling. NeuroImage 65, 540 (2013)CrossRefGoogle Scholar
  80. Shanahan, M.: Metastable chimera states in community-structured oscillator networks. Chaos 20, 013108 (2010)MathSciNetCrossRefGoogle Scholar
  81. Sporns, O.: Networks of the Brain. MIT Press, Cambridge (2011)zbMATHGoogle Scholar
  82. Sporns, O.: Structure and function of complex brain networks. Dialog. Clin. Neurosci. 15, 247 (2013)Google Scholar
  83. Sporns, O., Tononi, G., Kötter, R.: The human connectome: a structural description of the human brain. PLoS Comput. Biol. 1, e42 (2005)CrossRefGoogle Scholar
  84. Strogatz, S.H.: From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators. Physica D 143, 1 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  85. Tagliazucchi, E., Carhart-Harris, R., Leech, R., Nutt, D., Chialvo, D.R.: Enhanced repertoire of brain dynamical states during the psychedelic experience. Hum. Brain Mapp. 35, 5442 (2014)CrossRefGoogle Scholar
  86. Talairach, J., Tournoux, P.: Co-planar Stereotaxic Atlas of the Human Brain. 3-Dimensional Proportional System: An Approach to Cerebral Imaging. Thieme, New York (1988)Google Scholar
  87. Tognoli, E., Kelso, J.A.S.: The metastable brain. Neuron 81, 35 (2014)CrossRefGoogle Scholar
  88. Tzourio-Mazoyer, N., Landeau, B., Papathanassiou, D., Crivello, F., Etard, O., Delcroix, N., Mazoyer, B., Joliot, M.: Automated anatomical labeling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain. Neuroimage 15, 273 (2002)CrossRefGoogle Scholar
  89. Uhlhaas, P., Pipa, G., Lima, B., Melloni, L., Neuenschwander, S., Nikolic, D., Singer, W.: Neural synchrony in cortical networks: history, concept and current status. Front. Integr. Neurosci. 3, 17 (2009)CrossRefGoogle Scholar
  90. van den Heuvel, M.P., Hulshoff Pol, H.E.: Exploring the brain network: a review on resting-state fMRI functional connectivity. Eur. Neuropsychopharmacol. 20, 519 (2010)CrossRefGoogle Scholar
  91. Vása, F., Shanahan, M., Hellyer, P.J., Scott, G., Cabral, J., Leech, R.: Effects of lesions on synchrony and metastability in cortical networks. NeuroImage 118, 456 (2015)CrossRefGoogle Scholar
  92. Viol, A., Palhano-Fontes, F., Onias, H., de Araujo, D.B., Viswanathan, G.M.: Shannon entropy of brain functional complex networks under the influence of the psychedelic Ayahuasca. Sci. Rep. 7, 7388 (2017)CrossRefGoogle Scholar
  93. Vuksanović, V., Hövel, P.: Functional connectivity of distant cortical regions: role of remote synchronization and symmetry in interactions. NeuroImage 97, 1 (2014)CrossRefGoogle Scholar
  94. Vuksanović, V., Hövel, P.: Dynamic changes in network synchrony reveal resting-state functional networks. Chaos 25, 023116 (2015)MathSciNetCrossRefGoogle Scholar
  95. Vuksanović, V., Hövel, P.: Large-scale neural network model for functional networks of the human cortex. In: Pelster, A., Wunner, G. (eds.) Selforganization in Complex Systems: The Past, Present, and Future of Synergetics, Proceedings of the International Symposium, Hanse Institute of Advanced Studies Delmenhorst, pp. 345–352. Springer, Berlin (2016a). (Understanding Complex Systems)Google Scholar
  96. Vuksanović, V., Hövel, P.: Role of structural inhomogeneities in resting-state brain dynamics. Cogn. Neurodyn. 10, 361 (2016b)CrossRefGoogle Scholar
  97. Wang, Q.Y., Lu, Q.S.: Time delay-enhanced synchronization and regularization in two coupled chaotic neurons. Chin. Phys. Lett. 22, 543 (2005)CrossRefGoogle Scholar
  98. Wang, Q., Lu, Q., Chen, G.: Synchronization transition induced by synaptic delay in coupled fast-spiking neurons. Int. J. Bifur. Chaos 18, 1189 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  99. Wang, Q., Lu, Q., Chen, G., Feng, Z., Duan, L.X.: Bifurcation and synchronization of synaptically coupled FHN models with time delay. Chaos Solitons Fractals 39, 918 (2009)CrossRefGoogle Scholar
  100. Wildie, M., Shanahan, M.: Hierarchical clustering identifies hub nodes in a model of resting-state brain activity. In: The 2012 International Joint Conference on Neural Networks (IJCNN), pp. 1–6. IEEE (2012)Google Scholar
  101. Womelsdorf, T., Schoffelen, J.M., Oostenveld, R., Singer, W., Desimone, R.: Modulation of neuronal interactions through neuronal synchronization. Science 316, 1609 (2007)CrossRefGoogle Scholar
  102. Xia, M., Wang, J., He, Y.: Brainnet viewer: a network visualization tool for human brain connectomics. PLoS ONE 8, 1 (2013)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity College CorkCorkIreland
  2. 2.Institute of Theoretical PhysicsTechnische Universität BerlinBerlinGermany
  3. 3.Bernstein Center for Computational Neuroscience BerlinHumboldt-Universität zu BerlinBerlinGermany
  4. 4.Aberdeen Biomedical Imaging CentreUniversity of AberdeenAberdeenUK

Personalised recommendations