Advertisement

Effects of partial time delays on synchronization patterns in Izhikevich neuronal networks

  • Mohadeseh Shafiei
  • Fatemeh Parastesh
  • Mahdi Jalili
  • Sajad Jafari
  • Matjaž PercEmail author
  • Mitja Slavinec
Regular Article

Abstract

Synchronization patterns have been observed in neuronal networks and are related to many cognitive functions and information processing and even some pathological brain states. In this paper, we study a ring network of non-locally coupled Izhikevich neurons with electrical synaptic coupling. Since it has been proved that time delays through gap junctions can simplify the synchronization, here we particularly investigate the effects of partial time delays on networks synchronization. By using two control parameters, the time delay and the probability of partial time delay, we show that partial time delays have a significant effect on the synchronization of this network. In particular, partial time delays can either increase or decrease the synchronization and also can induce synchronization transitions between coherent and incoherent states. Thus, partial time delays can cause chimera state, which is a special pattern when both synchronous and asynchronous states coexist and are strongly related to many real phenomena. Furthermore, partial time delays can change the period of synchronized neurons from period-1 to period-2 firing states that have different effects on information transmission in the brain.

Graphical abstract

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    S. Krishnagopal, J. Lehnert, W. Poel, A. Zakharova, E. Schöll, Philos. Trans. R. Soc. A 375, 20160216 (2017) ADSCrossRefGoogle Scholar
  2. 2.
    P. Jaros, L. Borkowski, B. Witkowski, K. Czolczynski, T. Kapitaniak, Eur. Phys. J. Special Topics 224, 1605 (2015) ADSCrossRefGoogle Scholar
  3. 3.
    T. Chouzouris, I. Omelchenko, A. Zakharova, J. Hlinka, P. Jiruska, E. Schöll, Chaos 28, 045112 (2018) ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    M. Jalili, in International Conference on Information Management and Engineering, ICIMEˈ09 (IEEE, Piscataway, NJ, 2009), p. 17 Google Scholar
  5. 5.
    X. Sun, M. Perc, J. Kurths, Chaos 27, 053113 (2017) ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    I. Belykh, E. de Lange, M. Hasler, Phys. Rev. Lett. 94, 188101 (2005) ADSCrossRefGoogle Scholar
  7. 7.
    B. Tadić, M. Andjelković, B.M. Boshkoska, Z. Levnajić, PloS One 11, e0166787 (2016) CrossRefGoogle Scholar
  8. 8.
    M. Jalili, Physica A 466, 325 (2017) ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    J. Tang, J. Ma, M. Yi, H. Xia, X. Yang, Phys. Rev. E 83, 046207 (2011) ADSCrossRefGoogle Scholar
  10. 10.
    J. Ma, J. Tang, Nonlinear Dynam. 89, 1569 (2017) MathSciNetCrossRefGoogle Scholar
  11. 11.
    S. Achuthan, C.C. Canavier, J. Neurosci. 29, 5218 (2009) CrossRefGoogle Scholar
  12. 12.
    Z. Levnajić, A. Pikovsky, Phys. Rev. E 82, 056202 (2010) ADSCrossRefGoogle Scholar
  13. 13.
    Y.S. Cho, T. Nishikawa, A.E. Motter, Phys. Rev. Lett. 119, 084101 (2017) ADSCrossRefGoogle Scholar
  14. 14.
    S. Rakshit, B.K. Bera, M. Perc, D. Ghosh, Sci. Rep. 7, 2412 (2017) ADSCrossRefGoogle Scholar
  15. 15.
    Z. Faghani, Z. Arab, F. Parastesh, S. Jafari, M. Perc, M. Slavinec, Chaos Soliton. Fract. 114, 306 (2018) ADSCrossRefGoogle Scholar
  16. 16.
    Z.G. Nicolaou, H. Riecke, A.E. Motter, Phys. Rev. Lett. 119, 244101 (2017) ADSCrossRefGoogle Scholar
  17. 17.
    C. Wang, M. Lv, A. Alsaedi, J. Ma, Chaos 27, 113108 (2017) ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    J. Ma, F. Wu, C. Wang, Int. J. Mod. Phys. B 31, 1650251 (2017) ADSCrossRefGoogle Scholar
  19. 19.
    F. Parastesh, S. Jafari, H. Azarnoush, B. Hatef, A. Bountis, Chaos Soliton. Fract. 110, 203 (2018) ADSCrossRefGoogle Scholar
  20. 20.
    I. Omelchenko, E. Omelˈchenko, A. Zakharova, E. Schöll, Phys. Rev. E 97, 012216 (2018) ADSCrossRefGoogle Scholar
  21. 21.
    A. Mishra, S. Saha, P.K. Roy, T. Kapitaniak, S.K. Dana, Chaos 27, 023110 (2017) ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    Y. Maistrenko, S. Brezetsky, P. Jaros, R. Levchenko, T. Kapitaniak, Phys. Rev. E 95, 010203 (2017) ADSCrossRefGoogle Scholar
  23. 23.
    D. Dudkowski, Y. Maistrenko, T. Kapitaniak, Chaos 26, 116306 (2016) ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    J. Wojewoda, K. Czolczynski, Y. Maistrenko, T. Kapitaniak, Sci. Rep. 6, 34329 (2016) ADSCrossRefGoogle Scholar
  25. 25.
    R. Mukherjee, A. Sen, Chaos 28, 053109 (2018) ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    F.P. Kemeth, S.W. Haugland, K. Krischer, Phys. Rev. Lett. 120, 214101 (2018) ADSCrossRefGoogle Scholar
  27. 27.
    J.F. Totz, J. Rode, M.R. Tinsley, K. Showalter, H. Engel, Nat. Phys. 14, 282 (2018) CrossRefGoogle Scholar
  28. 28.
    M. Bolotov, L. Smirnov, G. Osipov, A. Pikovsky, Chaos 28, 045101 (2018) ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    S. Majhi, M. Perc, D. Ghosh, Chaos 27, 073109 (2017) ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    J. Ma, F. Wu, C. Wang, Int. J. Mod. Phys. B 31, 1650251 (2017) ADSCrossRefGoogle Scholar
  31. 31.
    S. Rakshit, A. Ray, B.K. Bera, D. Ghosh, Nonlinear Dynam. 94, 785 (2018) CrossRefGoogle Scholar
  32. 32.
    C.K. Volos, D. Prousalis, I.M. Kyprianidis, I. Stouboulos, S. Vaidyanathan, V.T. Pham, Int. J. Control Theory Appl. 9, 101 (2016) Google Scholar
  33. 33.
    Z. Wei, F. Parastesh, H. Azarnoush, S. Jafari, D. Ghosh, M. Perc, M. Slavinec, Europhys. Lett. 123, 48003 (2018) CrossRefGoogle Scholar
  34. 34.
    A. Schmidt, T. Kasimatis, J. Hizanidis, A. Provata, P. Hövel, Phys. Rev. E 95, 032224 (2017) ADSMathSciNetCrossRefGoogle Scholar
  35. 35.
    I. Omelchenko, A. Provata, J. Hizanidis, E. Schöll, P. Hövel, Phys. Rev. E 91, 022917 (2015) ADSMathSciNetCrossRefGoogle Scholar
  36. 36.
    J.M. Sausedo-Solorio, A.N. Pisarchik, Eur. Phys. J. Special Topics 226, 1911 (2017) ADSCrossRefGoogle Scholar
  37. 37.
    J.L. Wang, H.N. Wu, T. Huang, Automatica 56, 105 (2015) CrossRefGoogle Scholar
  38. 38.
    Z. Levnajić, B. Tadić, J. Stat. Mech. Theory Exp. 3, P03003 (2018) Google Scholar
  39. 39.
    H. Gu, Z. Zhao, PloS One 10, e0138593 (2015) CrossRefGoogle Scholar
  40. 40.
    Y. Çakir, Turk. J. Electr. Eng. Comp. Sci. 25, 2595 (2017) CrossRefGoogle Scholar
  41. 41.
    E. Rossoni, Y. Chen, M. Ding, J. Feng, Phys. Rev. E 71, 061904 (2005) ADSMathSciNetCrossRefGoogle Scholar
  42. 42.
    M. Masoliver, N. Malik, E. Schöll, A. Zakharova, Chaos 27, 101102 (2017) ADSMathSciNetCrossRefGoogle Scholar
  43. 43.
    M. Jalili, Neurocomputing 74, 1551 (2011) CrossRefGoogle Scholar
  44. 44.
    M. Jalili, Chaos 23, 013146 (2013) ADSMathSciNetCrossRefGoogle Scholar
  45. 45.
    A. Zakharova, N. Semenova, V. Anishchenko, E. Schöll, Chaos 27, 114320 (2017) ADSMathSciNetCrossRefGoogle Scholar
  46. 46.
    A. Gjurchinovski, E. Schöll, A. Zakharova, Phys. Rev. E 95, 042218 (2017) ADSMathSciNetCrossRefGoogle Scholar
  47. 47.
    S. Nobukawa, H. Nishimura, T. Yamanishi, Sci. Rep. 7, 1331 (2017) ADSCrossRefGoogle Scholar
  48. 48.
    Y. Hao, Y. Gong, L. Wang, X. Ma, C. Yang, Chaos Soliton. Fract. 44, 260 (2011) ADSCrossRefGoogle Scholar
  49. 49.
    M.V. Bennett, R.S. Zukin, Neuron 41, 495 (2004) CrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Biomedical Engineering Department, Amirkabir University of TechnologyTehranIran
  2. 2.School of Engineering, RMIT UniversityMelbourneAustralia
  3. 3.Faculty of Natural Sciences and Mathematics, University of MariborMariborSlovenia
  4. 4.Complexity Science Hub ViennaViennaAustria

Personalised recommendations