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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D.-U. Hwang, Phys. Rep. 424, 175 (2006)
S.H. Strogatz, Nature 410, 268 (2001)
R. Albert, A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002)
M.E.J. Newman, SIAM Rev. 45, 167 (2003)
A. Barrat, M. Barthélemy, A. Vespignani, Dynamical Processes on Complex Networks (Cambridge Univ. Press, 2008)
B. Barzel, A.-L. Barabási, Nat. Phys. 9, 673 (2013)
R. Banerjee, D. Ghosh, E. Padmanaban, R. Ramaswamy, L.M. Pecora, S.K. Dana, Phys. Rev. E 85, 027201 (2012)
S. Boccaletti, The Synchronized Dynamics of Complex Systems (Elsevier, Amsterdam, 2008), Vol. 6
S. Majhi, D. Ghosh, Chaos 27, 053115 (2017)
A. Arenas, A. Diaz-Guilera, J. Kurths, Y. Moreno, C. Zhou, Phys. Rep. 469, 93 (2008)
D. Ghosh, S. Banerjee, Phys. Rev. E 78, 056211 (2008)
D. Ghosh, P. Saha, A. Roy Chowdhury, Commun. Nonlinear Sci. Numer. Simul. 15, 1640 (2010)
A. Pikovsky, J. Kurths, M. Rosenblum, Synchronization: A Universal Concept in Nonlinear Sciences (Cambridge University Press, Cambridge, 2013)
P. Erdös, A. Rényi, Publ. Math. Debrecen 6, 290 (1959)
R. Albert, A.-L. Barabási, Science 286, 590 (1999)
D.J. Watts, S.H. Strogatz, Nature 393, 440 (1998)
F. Sorrentino, New J. Phys. 14, 033035 (2012)
S. Rakshit, B.K. Bera, D. Ghosh, Phys. Rev. E 98, 032305 (2018)
S. Rakshit, B.K. Bera, D. Ghosh, S. Sinha, Phys. Rev. E 97, 052304 (2018)
B.L.M. Happel, J.M.J. Murre, Neural Netw. 7, 985 (1994)
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)
M. Kivelä, A. Arenas, M. Barthelemy, J.P. Gleeson, Y. Moreno, M.A. Porter, J. Complex Networks 2, 203 (2014)
G. Bianconi, Multilayer Networks: Structure and Function (Oxford University Press, Oxford, 2018)
S. Pilosof, M.A. Porter, M. Pascual, S. Kéfi, Nat. Ecol. Evol. 1, 0101 (2017)
O. Yagan, D. Qian, J. Zhang, D. Cochran, IEEE J. Sel. Areas Commun 31, 1038 (2013)
A.E. Pereda, Nat. Rev. 15, 250 (2014)
M. Szell, R. Lambiotte, S. Thurner, Proc. Natl. Acad. Sci. USA 107, 13636 (2010)
A. Cardillo, J. Gómez-Gardeñes, M. Zanin, M. Romance, D. Papo, F. del Pozo, S. Boccaletti, Sci. Rep. 3, 1344 (2013)
A. Halu, S. Mukherjee, G. Bianconi, Phys. Rev. E 89, 012806 (2014)
A. Cardillo, M. Zanin, J. Gómez-Gardeñes, M. Romance, A. Garca del Amo, S. Boccaletti, Eur. Phys. J. Special Topics 215, 23 (2013)
R. Criado, M. Romance, M. Vela-Pérez, Int. J. Bifurc. Chaos 20 (2010) 877.
R. Criado, B. Hernández-Bermejo, M. Romance, Int. J. Bifurc. Chaos 17, 2289 (2007)
C. Granell, S. Gómez, A. Arenas, Phys. Rev. Lett. 111, 128701 (2013)
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)
S.V. Buldyrev, R. Parshani, G. Paul, H.E. Stanley, S. Havlin, Nature 464, 1025 (2010)
J. Gao, S.V. Buldyrev, H.E. Stanley, S. Havlin, Nat. Phys. 8, 40 (2012)
G. Bianconi, S.N. Dorogovtsev, Phys. Rev. E 89, 062814 (2014)
S. Gómez, A. Daz-Guilera, J. Gómez-Gardeñes, C.J. Pérez-Vicente, Y. Moreno, A. Arenas, Phys. Rev. Lett. 110, 028701 (2013)
A. Saumell-Mendiola, M. Serrano, M. Boguñá, Phys. Rev. E 86, 026106 (2012)
C. Buono, L.G. Alvarez-Zuzek, P.A. Macri, L.A. Braunstein, PLoS One 9, e92200 (2014)
J. Sanz, C.-Y. Xia, S. Meloni, Y. Moreno, Phys. Rev. X 4, 041005 (2014)
Z. Wang, A. Szolnoki, M. Perc, J. Theor. Biol. 349, 50 (2014)
G. Menichetti, L. Dall’Asta, G. Bianconi, Sci. Rep. 6, 20706 (2016)
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)
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)
L.V. Gambuzza, M. Frasca, J. Gómez-Gardeñes, Europhys. Lett. 110, 20010 (2015)
S. Rakshit, S. Majhi, B.K. Bera, S. Sinha, D. Ghosh, Phys. Rev. E 96, 062308 (2017)
S. Majhi, D. Ghosh, J. Kurths, Phys. Rev. E 99, 012308 (2019)
R. Sevilla-Escoboza, I. Sendiña-Nadal, I. Leyva, R. Gutiérrez, J.M. Buldú, S. Boccaletti, Chaos 26, 065304 (2016)
I. Leyva, R. Sevilla-Escoboza, I. Sendiña-Nadal, R. Gutiérrez, J.M. Buldú, S. Boccaletti, Sci. Rep. 7, 45475 (2017)
X. Zhang, S. Boccaletti, S. Guan, Z. Liu, Phys. Rev. Lett. 114, 038701 (2015)
S. Majhi, T. Kapitaniak, D. Ghosh, Chaos 29, 013108 (2019)
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)
S. Majhi, M. Perc, D. Ghosh, Sci. Rep. 6, 39033 (2016)
S. Majhi, B.K. Bera, D. Ghosh, M. Perc, Phys. Life Rev. 28, 100 (2019)
S. Majhi, M. Perc, D. Ghosh, Chaos 27, 073109 (2017)
S. Jalan, A. Singh, Europhys. Lett. 113, 30002 (2016)
P.J. Uhlhaas, G. Pipa, B. Lima, L. Melloni, S. Neuenschwander, D. Nikolić, W. Singer, Front. Integr. Neurosci. 3, 17 (2009)
B.K. Bera, D. Ghosh, M. Lakshmanan Phys. Rev. E 93, 012205 (2016)
B.K. Bera, D. Ghosh, T. Banerjee, Phys. Rev. E 94, 012215 (2016)
B.K. Bera, D. Ghosh, Phys. Rev. E 93, 052223 (2016)
P.J. Uhlhaas, W. Singer, Neuron 52, 155 (2006)
R. Llinas, U. Ribary, Proc. Natl. Acad. Sci. USA 90, 2078 (1993)
W. Singer, C.M. Gray, Annu. Rev. Neurosci. 18, 555 (1995)
D.K. Hartline, Biol. Cybern. 33, 223 (1979)
R. Bartsch, J.W. Kantelhardt, T. Penzel, S. Havlin, Phys. Rev. Lett. 98, 054102 (2007)
D.S. Bassett, E.D. Bullmore, Neuroscientist 12, 512 (2006)
D.S. Bassett, E.D. Bullmore, Neuroscientist 23, 499 (2017)
W.J. Yuan, J.F. Zhou, I.S. Nadal, S. Boccaletti, Z. Wang, Phys. Rev. E 97, 022211 (2018)
I. Leyva, I.S. Nadal, R.S. Escoboza, V.P. Vera-Avila, P. Chholak, S. Boccaletti, Sci. Rep. 8, 8629 (2018)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjst/e2019-900007-8