Remote synchronization in human cerebral cortex network with identical oscillators

  • Ling KangEmail author
  • Zhenhua Wang
  • Siyu Huo
  • Changhai Tian
  • Zonghua Liu
Original paper


Remote synchronization (RS) has recently received an increasing interest in the systems of nonidentical oscillators, but little attention has been paid to the systems of identical oscillators such as the case of human cerebral cortex where RS takes a key role in the functions of brain. Based on the real network of human cerebral cortex, we here show that RS can be also observed in the systems of identical oscillators, provided that appropriate time delay is considered. We interestingly find that RS may appear in different local places of cerebral cortex and thus results in a diversity of patterns, i.e., a new framework of multiple starlike graphs connected by common leaf nodes. To understand its mechanism, we present a model of two starlike graphs connected by common leaf nodes. We further show that the common leaf nodes take a key role for the emergence of RS in the new framework. A theoretical analysis is given. These findings may be helpful to understand the segregation and integration processes of information transmission in brain.


Remote synchronization Human cerebral cortex Time delay Common leaf node 



This work was partially supported by the NNSF of China under Grant Nos. 11675056 and 11835003.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no competing interests.


  1. 1.
    Ito, T., Kulkarni, K.R., Schultz, D.H., Mill, R.D., Chen, R.H., Solomyak, L.I., Cole, M.W.: Cognitive task information is transferred between brain regions via resting-state network topology. Nat. Commun. 8, 1027 (2017)CrossRefGoogle Scholar
  2. 2.
    Del Ferraro, G., Moreno, A., Min, B., Morone, F., Perez-Ramirez, U., Perez-Cervera, L., Parra, L.C., Holodny, A., Canals, S., Makse, H.A.: Finding influential nodes for integration in brain networks using optimal percolation theory. Nat. Commun. 9, 2274 (2018)CrossRefGoogle Scholar
  3. 3.
    Hagmann, P., Cammoun, L., Gigandet, X., Meuli, R., Honey, C.J., Wedeen, V.J., Sporns, O.: Mapping the structural core of human cerebral cortex. PLoS Biol. 6, 1479 (2008)CrossRefGoogle Scholar
  4. 4.
    Ma, J., Tang, J.: A review for dynamics in neuron and neuronal network. Nonlinear Dyn. 89, 1569 (2017)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Jia, Y., Gu, H.: Identifying nonlinear dynamics of brain functional networks of patients with schizophrenia by sample entropy. Nonlinear Dyn. 96, 2327 (2019)CrossRefGoogle Scholar
  6. 6.
    Liu, Z., Wang, C., Jin, W., Ma, J.: Capacitor coupling induces synchronization between neural circuits. Nonlinear Dyn. 97, 2661 (2019)CrossRefGoogle Scholar
  7. 7.
    Ozer, M., Uzuntarla, M., Agaoglu, S.N.: Effect of the sub-threshold periodic current forcing on the regularity and the synchronization of neuronal spiking activity. Phys. Lett. A 360, 135 (2006)CrossRefGoogle Scholar
  8. 8.
    Uzuntarla, M., Torres, J.J., Calim, A., Barreto, E.: Synchronization-induced spike termination in networks of bistable neurons. Neural Netw. 110, 131 (2019)CrossRefGoogle Scholar
  9. 9.
    Sporns, O.: Network attributes for segregation and integration in the human brain. Curr. Opin. Neurobiol. 23, 162 (2013)CrossRefGoogle Scholar
  10. 10.
    Park, H.J., Friston, K.: Structural and functional brain networks: from connections to cognition. Science 342, 6158 (2013)CrossRefGoogle Scholar
  11. 11.
    Bullmore, E., Sporns, O.: Complex brain networks: graph theoretical analysis of structural and functional systems. Nat. Rev. Neurosci. 10, 186 (2009)CrossRefGoogle Scholar
  12. 12.
    Sporns, O.: Contributions and challenges for network models in cognitive neuroscience. Nat. Neurosci. 17, 652 (2014)CrossRefGoogle Scholar
  13. 13.
    Hipp, J.F., Engel, A.K., Siegel, M.: Oscillatory synchronization in large-scale cortical networks predicts perception. Neuron 69, 387 (2011)CrossRefGoogle Scholar
  14. 14.
    Roelfsema, P.R., Engel, A.K., Konig, P., Singer, W.: Visuomotor integration is associated with zero time-lag synchronization among cortical areas. Nature 385, 157 (1997)CrossRefGoogle Scholar
  15. 15.
    Vogels, T.P., Abbott, L.F.: Signal propagation and logic gating in networks of integrate-and-fire neurons. Neuroscience 25, 10786 (2005)CrossRefGoogle Scholar
  16. 16.
    Diesmann, M., Gewaltig, M.O., Aertsen, A.: Stable propagation of synchronous spiking in cortical neural networks. Nature 402, 529 (1999)CrossRefGoogle Scholar
  17. 17.
    Singer, W.: Neuronal synchrony: a versatile code for the definition of relations? Neuron 24, 49 (1999)CrossRefGoogle Scholar
  18. 18.
    Womelsdorf, T., Schoffelen, J.M., Oostenveld, R., Singer, W., Desimone, R., Engel, A.K., Fries, P.: Modulation of neuronal interactions through neuronal synchronization. Science 316, 1609 (2007)CrossRefGoogle Scholar
  19. 19.
    Arenas, A., Diaz-Guilera, A., Kurths, J., Moreno, Y., Zhou, C.: Synchronization in complex networks. Phys. Rep. 469, 93 (2008)MathSciNetCrossRefGoogle Scholar
  20. 20.
    van Vreeswijk, C.: Partial synchronization in populations of pulse-coupled oscillators. Phys. Rev. E 54, 5522 (1996)CrossRefGoogle Scholar
  21. 21.
    Bansal, K., Garcia, J.O., Tompson, S.H., Verstynen, T., Vettel, J.M., Muldoon, S.F.: Cognitive chimera states in human brain networks. Sci. Adv. 5, eaau8535 (2019)CrossRefGoogle Scholar
  22. 22.
    Abrams, D.M., Strogatz, S.H.: Chimera states for coupled oscillators. Phys. Rev. Lett. 93, 174102 (2004)CrossRefGoogle Scholar
  23. 23.
    Abrams, D.M., Mirollo, R., Strogatz, S.H., Wiley, D.A.: Solvable model for chimera states of coupled oscillators. Phys. Rev. Lett. 101, 084103 (2008)CrossRefGoogle Scholar
  24. 24.
    Tian, C., Cao, L., Bi, H., Xu, K., Liu, Z.: Chimera states in neuronal networks with time delay and electromagnetic induction. Nonlinear Dyn. 93, 1695 (2018)CrossRefGoogle Scholar
  25. 25.
    Huo, S., Tian, C., Kang, L., Liu, Z.: Chimera states of neuron networks with adaptive coupling. Nonlinear Dyn. 96, 75 (2019)CrossRefGoogle Scholar
  26. 26.
    Calim, A., Hovel, P., Ozer, M., Uzuntarla, M.: Chimera states in networks of type-I Morris–Lecar neurons. Phys. Rev. E 98, 062217 (2018)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Rattenborg, N.C., Amlaner, C.J., Lima, S.L.: Behavioral, neurophysiological and evolutionary perspectives on unihemispheric sleep. Neurosci. Biobehav. Rev. 24, 817 (2000)CrossRefGoogle Scholar
  28. 28.
    Mathews, C.G., Lesku, J.A., Lima, S.L., Amlaner, C.J.: Asynchronous eye closure as an anti-predator behavior in the western fence lizard (Sceloporus occidentalis. Ethology 112, 286 (2006)CrossRefGoogle Scholar
  29. 29.
    Pikovsky, A., Rosenblum, M.: Partially integrable dynamics of hierarchical populations of coupled oscillators. Phys. Rev. Lett. 101, 264103 (2008)CrossRefGoogle Scholar
  30. 30.
    Ma, R., Wang, J., Liu, Z.: Robust features of chimera states and the implementation of alternating chimera states. Europhys. Lett. 91, 40006 (2010)CrossRefGoogle Scholar
  31. 31.
    Tamaki, M., Bang, J.W., Watanabe, T., Sasaki, Y.: Night watch in one brain hemisphere during sleep associated with the first-night effect in humans. Curr. Biol. 26, 1190 (2016)CrossRefGoogle Scholar
  32. 32.
    Schaub, M.T., O’Clery, N., Billeh, Y.N., Delvenne, J.C., Lambiotte, R., Barahona, M.: Graph partitions and cluster synchronization in networks of oscillators. Chaos 26, 094821 (2016)MathSciNetzbMATHCrossRefGoogle Scholar
  33. 33.
    Cao, B., Wang, Y.F., Wang, L., Yu, Y.Z., Wang, X.G.: Cluster synchronization in complex network of coupled chaotic circuits: an experimental study. Front. Phys. 13, 130505 (2018)CrossRefGoogle Scholar
  34. 34.
    Sorrentino, F., Pecora, L.M., Hagerstrom, A.M., Murphy, T.E., Roy, R.: Complete characterization of the stability of cluster synchronization in complex dynamical networks. Sci. Adv. 2, e1501737 (2016)CrossRefGoogle Scholar
  35. 35.
    Pecora, L.M., Sorrentino, F., Hagerstrom, A.M., Murphy, T.E., Roy, R.: Cluster synchronization and isolated desynchronization in complex networks with symmetries. Nat. Commun. 5, 4079 (2014)CrossRefGoogle Scholar
  36. 36.
    Siddique, A.B., Pecora, L., Hart, J.D., Sorrentino, F.: Symmetry-and input-cluster synchronization in networks. Phys. Rev. E 97, 042217 (2018)CrossRefGoogle Scholar
  37. 37.
    Williams, C.R., Murphy, T.E., Roy, R., Sorrentino, F., Dahms, T., Schöll, E.: Experimental observations of group synchrony in a system of chaotic optoelectronic oscillators. Phys. Rev. Lett. 110, 064104 (2013)CrossRefGoogle Scholar
  38. 38.
    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
  39. 39.
    Minati, L.: Remote synchronization of amplitudes across an experimental ring of non-linear oscillators. Chaos 25, 123107 (2015)MathSciNetzbMATHCrossRefGoogle Scholar
  40. 40.
    Hart, J.D., Bansal, K., Murphy, T.E., Roy, R.: Experimental observation of chimera and cluster states in a minimal globally coupled network. Chaos 26, 094801 (2016)MathSciNetCrossRefGoogle Scholar
  41. 41.
    Cho, Y.S., Nishikawa, T., Motter, A.E.: Stable chimeras and independently synchronizable clusters. Phys. Rev. Lett. 119, 084101 (2017)CrossRefGoogle Scholar
  42. 42.
    Schmidt, L., Krischer, K.: Clustering as a prerequisite for chimera states in globally coupled systems. Phys. Rev. Lett. 114, 034101 (2015)CrossRefGoogle Scholar
  43. 43.
    Majhi, S., Perc, M., Ghosh, D.: Chimera states in a multilayer network of coupled and uncoupled neurons. Chaos 27, 073109 (2017)MathSciNetCrossRefGoogle Scholar
  44. 44.
    Bassett, D.S., Bullmore, E.D.: Small-world brain networks. Neuroscientist 12, 512 (2006)CrossRefGoogle Scholar
  45. 45.
    Perl, E.R.: The Thalamus. Cambridge University Press, Cambridge (2007)Google Scholar
  46. 46.
    Viriyopase, A., Bojak, I., Zeitler, M., Gielen, S.: When long-range zero-lag synchronization is feasible in cortical networks. Front. Comput. Neurosci. 6, 49 (2012)CrossRefGoogle Scholar
  47. 47.
    Fischer, I., Vicente, R., Buldu, J.M., Peil, M., Mirasso, C.R., Torrent, M.C., Garcia-Ojalvo, J.: Zero-lag long-range synchronization via dynamical relaying. Phys. Rev. Lett. 97, 123901 (2006)CrossRefGoogle Scholar
  48. 48.
    Vicente, R., Gollo, L.L., Mirasso, C.R., Fischer, I., Pipa, G.: Dynamical relaying can yield zero time lag neuronal synchrony despite long conduction delays. Proc. Natl. Acad. Sci. USA 105, 17157 (2008)CrossRefGoogle Scholar
  49. 49.
    Sherman, S.M., Guillery, R.W.: Exploring the Thalamus and Its Role in Cortical Function. Academic Press, Cambridge, MA (2006)Google Scholar
  50. 50.
    Lagier, S., Carleton, A., Lledo, P.M.: Interplay between local GABAergic interneurons and relay neurons generates \(\gamma \) oscillations in the rat olfactory bulb. J. Neurosci. 24, 4382 (2004)CrossRefGoogle Scholar
  51. 51.
    Seki, K., Perlmutter, S.I., Fetz, E.E.: Sensory input to primate spinal cord is presynaptically inhibited during voluntary movement. Nat. Neurosci. 6, 1309 (2003)CrossRefGoogle Scholar
  52. 52.
    Vlasov, V., Bifone, A.: Hub-driven remote synchronization in brain networks. Sci. Rep. 7, 10403 (2017)CrossRefGoogle Scholar
  53. 53.
    Gambuzza, L.V., Cardillo, A., Fiasconaro, A., Fortuna, L., Gomez-Gardenes, J., Frasca, M.: Analysis of remote synchronization in complex networks. Chaos 23, 043103 (2013)zbMATHCrossRefGoogle Scholar
  54. 54.
    Gambuzza, L.V., Frasca, M., Fortuna, L., Boccaletti, S.: Inhomogeneity induces relay synchronization in complex networks. Phys. Rev. E 93, 042203 (2016)CrossRefGoogle Scholar
  55. 55.
    Nicosia, V., Valencia, M., Chavez, M., Diaz-Guilera, A., Latora, V.: Remote synchronization reveals network symmetries and functional modules. Phys. Rev. Lett. 110, 174102 (2013)CrossRefGoogle Scholar
  56. 56.
    Hagmann, P., Kurant, M., Gigandet, X., Thiran, P., Wedeen, V.J., Meuli, R., Thiran, J.P.: Mapping human whole-brain structural networks with diffusion MRI. PLoS ONE 2, e597 (2007)CrossRefGoogle Scholar
  57. 57.
    Iturria-Medina, Y., Sotero, R.C., Canales-Rodriguez, E.J., Aleman-Gomez, Y., Melie-Garcia, L.: Studying the human brain anatomical network via diffusion-weighted MRI and graph theory. Neuroimage 40, 1064 (2007)CrossRefGoogle Scholar
  58. 58.
    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
  59. 59.
    Aguirre, G.K., Zarahn, E., D’esposito, M.: The inferential impact of global signal covariates in functional neuroimaging analyses. Neuroimage 8, 302 (1998)CrossRefGoogle Scholar
  60. 60.
    Izhikevich, E.M.: Polychronization: computation with spikes. Neural Comput. 18, 245 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  61. 61.
    Adhikari, B.M., Prasad, A., Dhamala, M.: Time-delay-induced phase-transition to synchrony in coupled bursting neurons. Chaos 21, 023116 (2011)MathSciNetCrossRefGoogle Scholar
  62. 62.
    Dhamala, M., Jirsa, V.K., Ding, M.: Enhancement of neural synchrony by time delay. Phys. Rev. Lett. 92, 074104 (2004)CrossRefGoogle Scholar
  63. 63.
    Wendling, F., Bellanger, J.J., Bartolomei, F., Chauvel, P.: Relevance of nonlinear lumped-parameter models in the analysis of depth-EEG epileptic signals. Biol. Cybern. 83, 367 (2000)CrossRefGoogle Scholar
  64. 64.
    Zhou, C., Zemanova, L., Zamora-Lopez, G., Hilgetag, C.C., Kurths, J.: Structure function relationship in complex brain networks expressed by hierarchical synchronization. New J. Phys. 9, 178 (2007)CrossRefGoogle Scholar
  65. 65.
    Wilson, H.R., Cowan, J.D.: Excitatory and inhibitory interactions in localized populations of model neurons. Biophys J. 12, 1 (1972)CrossRefGoogle Scholar
  66. 66.
    Daffertshofer, A., van Wijk, B.C.M.: On the influence of amplitude on the connectivity between phases. Front Neuroinform. 5, 8 (2011)CrossRefGoogle Scholar
  67. 67.
    Hoppensteadt, F.C., Izhikevich, E.M.: Weakly Connected Neural Networks, 1st edn. Springer, New York (1997)zbMATHCrossRefGoogle Scholar
  68. 68.
    Sherman, A., Rinzel, J.: Rhythmogenic effects of weak electrotonic coupling in neuronal models. Proc. Natl. Acad. Sci. USA 89, 2471 (1992)CrossRefGoogle Scholar
  69. 69.
    Steyn-Ross, D.A., Steyn-Ross, M., Freeman, W. (eds.): Modeling Phase Transitions in the Brain, 1st edn. Springer, New York (2010)zbMATHGoogle Scholar
  70. 70.
    Moon, J., Lee, U., Blain-Moraes, S., Mashour, G.A.: General relationship of global topology, local dynamics, and directionality in large-scale brain networks. PLOS Comput. Biol. 11, e1004225 (2015)CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of PhysicsEast China Normal UniversityShanghaiChina
  2. 2.School of Data ScienceTongren UniversityTongrenChina

Personalised recommendations