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Intralayer synchronization in neuronal multiplex network

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Abstract

Synchronization phenomenon is one of the most fundamental properties in the field of neurosciences, and it plays a key role in several neuronal processes. In this paper, we report a neural synchrony in a multiplex neuronal network by simultaneously taking electrical and chemical synaptic interactions. Most of the previous studies on the neuronal synchrony have been focused on a mono-layer network by solely considering one type of neuronal communication, either electrical or chemical synaptic coupling. Here we consider the multiplex network where the connection within the layer (intralayer connection) and the layer–layer interaction (interlayer connection) links are associated with the electrical and chemical synapses respectively. The network topology in each layer is represented by the small-world network. We mainly explore intralayer synchronization in the multiplex network under the simultaneous effect of both synaptic interactions. Intralayer synchronization is a distinctive process that refered to coherence among the nodes within the layer irrespective of the coherence between the replica nodes. Through the master stability approach, we derive the necessary condition for the intralayer synchronization state and then we numerically confirm our analytical findings.

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References

  1. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D.-U. Hwang, Phys. Rep. 424, 175 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  2. S.H. Strogatz, Nature 410, 268 (2001)

    Article  ADS  Google Scholar 

  3. R. Albert, A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  4. M.E.J. Newman, SIAM Rev. 45, 167 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  5. A. Barrat, M. Barthélemy, A. Vespignani, Dynamical Processes on Complex Networks (Cambridge Univ. Press, 2008)

  6. B. Barzel, A.-L. Barabási, Nat. Phys. 9, 673 (2013)

    Article  Google Scholar 

  7. R. Banerjee, D. Ghosh, E. Padmanaban, R. Ramaswamy, L.M. Pecora, S.K. Dana, Phys. Rev. E 85, 027201 (2012)

    Article  ADS  Google Scholar 

  8. S. Boccaletti, The Synchronized Dynamics of Complex Systems (Elsevier, Amsterdam, 2008), Vol. 6

    Google Scholar 

  9. S. Majhi, D. Ghosh, Chaos 27, 053115 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  10. A. Arenas, A. Diaz-Guilera, J. Kurths, Y. Moreno, C. Zhou, Phys. Rep. 469, 93 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  11. D. Ghosh, S. Banerjee, Phys. Rev. E 78, 056211 (2008)

    Article  ADS  Google Scholar 

  12. D. Ghosh, P. Saha, A. Roy Chowdhury, Commun. Nonlinear Sci. Numer. Simul. 15, 1640 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  13. A. Pikovsky, J. Kurths, M. Rosenblum, Synchronization: A Universal Concept in Nonlinear Sciences (Cambridge University Press, Cambridge, 2013)

  14. P. Erdös, A. Rényi, Publ. Math. Debrecen 6, 290 (1959)

    MathSciNet  Google Scholar 

  15. R. Albert, A.-L. Barabási, Science 286, 590 (1999)

    MathSciNet  Google Scholar 

  16. D.J. Watts, S.H. Strogatz, Nature 393, 440 (1998)

    Article  ADS  Google Scholar 

  17. F. Sorrentino, New J. Phys. 14, 033035 (2012)

    Article  ADS  Google Scholar 

  18. S. Rakshit, B.K. Bera, D. Ghosh, Phys. Rev. E 98, 032305 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  19. S. Rakshit, B.K. Bera, D. Ghosh, S. Sinha, Phys. Rev. E 97, 052304 (2018)

    Article  ADS  Google Scholar 

  20. B.L.M. Happel, J.M.J. Murre, Neural Netw. 7, 985 (1994)

    Article  Google Scholar 

  21. S. Boccaletti, G. Bianconi, R. Criado, C.I. del Genio, J. Gómez-Gardeñes, M. Romance, I. Sendiña-Nadal, Z. Wang, M. Zanin, Phys. Rep. 544, 1 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  22. M. Kivelä, A. Arenas, M. Barthelemy, J.P. Gleeson, Y. Moreno, M.A. Porter, J. Complex Networks 2, 203 (2014)

    Article  Google Scholar 

  23. G. Bianconi, Multilayer Networks: Structure and Function (Oxford University Press, Oxford, 2018)

  24. S. Pilosof, M.A. Porter, M. Pascual, S. Kéfi, Nat. Ecol. Evol. 1, 0101 (2017)

    Article  Google Scholar 

  25. O. Yagan, D. Qian, J. Zhang, D. Cochran, IEEE J. Sel. Areas Commun 31, 1038 (2013)

    Article  Google Scholar 

  26. A.E. Pereda, Nat. Rev. 15, 250 (2014)

    Article  Google Scholar 

  27. M. Szell, R. Lambiotte, S. Thurner, Proc. Natl. Acad. Sci. USA 107, 13636 (2010)

    Article  ADS  Google Scholar 

  28. A. Cardillo, J. Gómez-Gardeñes, M. Zanin, M. Romance, D. Papo, F. del Pozo, S. Boccaletti, Sci. Rep. 3, 1344 (2013)

    Article  Google Scholar 

  29. A. Halu, S. Mukherjee, G. Bianconi, Phys. Rev. E 89, 012806 (2014)

    Article  ADS  Google Scholar 

  30. A. Cardillo, M. Zanin, J. Gómez-Gardeñes, M. Romance, A. Garca del Amo, S. Boccaletti, Eur. Phys. J. Special Topics 215, 23 (2013)

    Article  ADS  Google Scholar 

  31. R. Criado, M. Romance, M. Vela-Pérez, Int. J. Bifurc. Chaos 20 (2010) 877.

    Article  Google Scholar 

  32. R. Criado, B. Hernández-Bermejo, M. Romance, Int. J. Bifurc. Chaos 17, 2289 (2007)

    Article  Google Scholar 

  33. C. Granell, S. Gómez, A. Arenas, Phys. Rev. Lett. 111, 128701 (2013)

    Article  ADS  Google Scholar 

  34. B. Bentley, R. Branicky, C.L. Barnes, Y.L. Chew, E. Yemini, E.T. Bullmore, P.E. Vértes, W.R. Schafer, PLoS Comput. Biol. 12, e1005283 (2016)

    Article  ADS  Google Scholar 

  35. S.V. Buldyrev, R. Parshani, G. Paul, H.E. Stanley, S. Havlin, Nature 464, 1025 (2010)

    Article  ADS  Google Scholar 

  36. J. Gao, S.V. Buldyrev, H.E. Stanley, S. Havlin, Nat. Phys. 8, 40 (2012)

    Article  Google Scholar 

  37. G. Bianconi, S.N. Dorogovtsev, Phys. Rev. E 89, 062814 (2014)

    Article  ADS  Google Scholar 

  38. S. Gómez, A. Daz-Guilera, J. Gómez-Gardeñes, C.J. Pérez-Vicente, Y. Moreno, A. Arenas, Phys. Rev. Lett. 110, 028701 (2013)

    Article  ADS  Google Scholar 

  39. A. Saumell-Mendiola, M. Serrano, M. Boguñá, Phys. Rev. E 86, 026106 (2012)

    Article  ADS  Google Scholar 

  40. C. Buono, L.G. Alvarez-Zuzek, P.A. Macri, L.A. Braunstein, PLoS One 9, e92200 (2014)

    Article  ADS  Google Scholar 

  41. J. Sanz, C.-Y. Xia, S. Meloni, Y. Moreno, Phys. Rev. X 4, 041005 (2014)

    Google Scholar 

  42. Z. Wang, A. Szolnoki, M. Perc, J. Theor. Biol. 349, 50 (2014)

    Article  Google Scholar 

  43. G. Menichetti, L. Dall’Asta, G. Bianconi, Sci. Rep. 6, 20706 (2016)

    Article  ADS  Google Scholar 

  44. M.V. Goremyko, V.A. Maksimenko, V.V. Makarov, D. Ghosh, B. Bera, S.K. Dana, A.E. Hramov, Tech. Phys. Lett. 43, 712 (2017)

    Article  ADS  Google Scholar 

  45. V.A. Maksimenko, M.V. Goremyko, V.V. Makarov, A.E. Hramov, D. Ghosh, B.K. Bera, S.K. Dana, Bull. Russ. Acad. Sci.: Phys. 81, 110 (2017)

    Article  Google Scholar 

  46. L.V. Gambuzza, M. Frasca, J. Gómez-Gardeñes, Europhys. Lett. 110, 20010 (2015)

    Article  ADS  Google Scholar 

  47. S. Rakshit, S. Majhi, B.K. Bera, S. Sinha, D. Ghosh, Phys. Rev. E 96, 062308 (2017)

    Article  ADS  Google Scholar 

  48. S. Majhi, D. Ghosh, J. Kurths, Phys. Rev. E 99, 012308 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  49. R. Sevilla-Escoboza, I. Sendiña-Nadal, I. Leyva, R. Gutiérrez, J.M. Buldú, S. Boccaletti, Chaos 26, 065304 (2016)

    Article  MathSciNet  Google Scholar 

  50. I. Leyva, R. Sevilla-Escoboza, I. Sendiña-Nadal, R. Gutiérrez, J.M. Buldú, S. Boccaletti, Sci. Rep. 7, 45475 (2017)

    Article  ADS  Google Scholar 

  51. X. Zhang, S. Boccaletti, S. Guan, Z. Liu, Phys. Rev. Lett. 114, 038701 (2015)

    Article  ADS  Google Scholar 

  52. S. Majhi, T. Kapitaniak, D. Ghosh, Chaos 29, 013108 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  53. V.A. Maksimenko, V.V. Makarov, B.K. Bera, D. Ghosh, S.K. Dana, M.V. Goremyko, N.S. Frolov, A.A. Koronovskii, A.E. Hramov, Phys. Rev. E 94, 052205 (2016)

    Article  ADS  Google Scholar 

  54. S. Majhi, M. Perc, D. Ghosh, Sci. Rep. 6, 39033 (2016)

    Article  ADS  Google Scholar 

  55. S. Majhi, B.K. Bera, D. Ghosh, M. Perc, Phys. Life Rev. 28, 100 (2019)

    Article  ADS  Google Scholar 

  56. S. Majhi, M. Perc, D. Ghosh, Chaos 27, 073109 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  57. S. Jalan, A. Singh, Europhys. Lett. 113, 30002 (2016)

    Article  Google Scholar 

  58. P.J. Uhlhaas, G. Pipa, B. Lima, L. Melloni, S. Neuenschwander, D. Nikolić, W. Singer, Front. Integr. Neurosci. 3, 17 (2009)

    Article  Google Scholar 

  59. B.K. Bera, D. Ghosh, M. Lakshmanan Phys. Rev. E 93, 012205 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  60. B.K. Bera, D. Ghosh, T. Banerjee, Phys. Rev. E 94, 012215 (2016)

    Article  ADS  Google Scholar 

  61. B.K. Bera, D. Ghosh, Phys. Rev. E 93, 052223 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  62. P.J. Uhlhaas, W. Singer, Neuron 52, 155 (2006)

    Article  Google Scholar 

  63. R. Llinas, U. Ribary, Proc. Natl. Acad. Sci. USA 90, 2078 (1993)

    Article  ADS  Google Scholar 

  64. W. Singer, C.M. Gray, Annu. Rev. Neurosci. 18, 555 (1995)

    Article  Google Scholar 

  65. D.K. Hartline, Biol. Cybern. 33, 223 (1979)

    Article  Google Scholar 

  66. R. Bartsch, J.W. Kantelhardt, T. Penzel, S. Havlin, Phys. Rev. Lett. 98, 054102 (2007)

    Article  ADS  Google Scholar 

  67. D.S. Bassett, E.D. Bullmore, Neuroscientist 12, 512 (2006)

    Article  Google Scholar 

  68. D.S. Bassett, E.D. Bullmore, Neuroscientist 23, 499 (2017)

    Article  Google Scholar 

  69. W.J. Yuan, J.F. Zhou, I.S. Nadal, S. Boccaletti, Z. Wang, Phys. Rev. E 97, 022211 (2018)

    Article  ADS  Google Scholar 

  70. I. Leyva, I.S. Nadal, R.S. Escoboza, V.P. Vera-Avila, P. Chholak, S. Boccaletti, Sci. Rep. 8, 8629 (2018)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar, 140001, Punjab, India

    Bidesh K. Bera

  2. Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, 700108, India

    Sarbendu Rakshit & Dibakar Ghosh

Authors
  1. Bidesh K. Bera
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  2. Sarbendu Rakshit
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  3. Dibakar Ghosh
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Correspondence to Dibakar Ghosh.

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Bera, B.K., Rakshit, S. & Ghosh, D. Intralayer synchronization in neuronal multiplex network. Eur. Phys. J. Spec. Top. 228, 2441–2454 (2019). https://doi.org/10.1140/epjst/e2019-900007-8

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  • DOI: https://doi.org/10.1140/epjst/e2019-900007-8

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