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

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.

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References

  1. S. Krishnagopal, J. Lehnert, W. Poel, A. Zakharova, E. Schöll, Philos. Trans. R. Soc. A 375, 20160216 (2017)

    Article  ADS  Google Scholar 

  2. P. Jaros, L. Borkowski, B. Witkowski, K. Czolczynski, T. Kapitaniak, Eur. Phys. J. Special Topics 224, 1605 (2015)

    Article  ADS  Google Scholar 

  3. T. Chouzouris, I. Omelchenko, A. Zakharova, J. Hlinka, P. Jiruska, E. Schöll, Chaos 28, 045112 (2018)

    MathSciNet  Article  ADS  Google Scholar 

  4. M. Jalili, in International Conference on Information Management and Engineering, ICIMEˈ09 (IEEE, Piscataway, NJ, 2009), p. 17

  5. X. Sun, M. Perc, J. Kurths, Chaos 27, 053113 (2017)

    MathSciNet  Article  ADS  Google Scholar 

  6. I. Belykh, E. de Lange, M. Hasler, Phys. Rev. Lett. 94, 188101 (2005)

    Article  ADS  Google Scholar 

  7. B. Tadić, M. Andjelković, B.M. Boshkoska, Z. Levnajić, PloS One 11, e0166787 (2016)

    Article  Google Scholar 

  8. M. Jalili, Physica A 466, 325 (2017)

    MathSciNet  Article  ADS  Google Scholar 

  9. J. Tang, J. Ma, M. Yi, H. Xia, X. Yang, Phys. Rev. E 83, 046207 (2011)

    Article  ADS  Google Scholar 

  10. J. Ma, J. Tang, Nonlinear Dynam. 89, 1569 (2017)

    MathSciNet  Article  Google Scholar 

  11. S. Achuthan, C.C. Canavier, J. Neurosci. 29, 5218 (2009)

    Article  Google Scholar 

  12. Z. Levnajić, A. Pikovsky, Phys. Rev. E 82, 056202 (2010)

    Article  ADS  Google Scholar 

  13. Y.S. Cho, T. Nishikawa, A.E. Motter, Phys. Rev. Lett. 119, 084101 (2017)

    Article  ADS  Google Scholar 

  14. S. Rakshit, B.K. Bera, M. Perc, D. Ghosh, Sci. Rep. 7, 2412 (2017)

    Article  ADS  Google Scholar 

  15. Z. Faghani, Z. Arab, F. Parastesh, S. Jafari, M. Perc, M. Slavinec, Chaos Soliton. Fract. 114, 306 (2018)

    Article  ADS  Google Scholar 

  16. Z.G. Nicolaou, H. Riecke, A.E. Motter, Phys. Rev. Lett. 119, 244101 (2017)

    Article  ADS  Google Scholar 

  17. C. Wang, M. Lv, A. Alsaedi, J. Ma, Chaos 27, 113108 (2017)

    MathSciNet  Article  ADS  Google Scholar 

  18. J. Ma, F. Wu, C. Wang, Int. J. Mod. Phys. B 31, 1650251 (2017)

    Article  ADS  Google Scholar 

  19. F. Parastesh, S. Jafari, H. Azarnoush, B. Hatef, A. Bountis, Chaos Soliton. Fract. 110, 203 (2018)

    Article  ADS  Google Scholar 

  20. I. Omelchenko, E. Omelˈchenko, A. Zakharova, E. Schöll, Phys. Rev. E 97, 012216 (2018)

    Article  ADS  Google Scholar 

  21. A. Mishra, S. Saha, P.K. Roy, T. Kapitaniak, S.K. Dana, Chaos 27, 023110 (2017)

    MathSciNet  Article  ADS  Google Scholar 

  22. Y. Maistrenko, S. Brezetsky, P. Jaros, R. Levchenko, T. Kapitaniak, Phys. Rev. E 95, 010203 (2017)

    Article  ADS  Google Scholar 

  23. D. Dudkowski, Y. Maistrenko, T. Kapitaniak, Chaos 26, 116306 (2016)

    MathSciNet  Article  ADS  Google Scholar 

  24. J. Wojewoda, K. Czolczynski, Y. Maistrenko, T. Kapitaniak, Sci. Rep. 6, 34329 (2016)

    Article  ADS  Google Scholar 

  25. R. Mukherjee, A. Sen, Chaos 28, 053109 (2018)

    MathSciNet  Article  ADS  Google Scholar 

  26. F.P. Kemeth, S.W. Haugland, K. Krischer, Phys. Rev. Lett. 120, 214101 (2018)

    Article  ADS  Google Scholar 

  27. J.F. Totz, J. Rode, M.R. Tinsley, K. Showalter, H. Engel, Nat. Phys. 14, 282 (2018)

    Article  Google Scholar 

  28. M. Bolotov, L. Smirnov, G. Osipov, A. Pikovsky, Chaos 28, 045101 (2018)

    MathSciNet  Article  ADS  Google Scholar 

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

    MathSciNet  Article  ADS  Google Scholar 

  30. J. Ma, F. Wu, C. Wang, Int. J. Mod. Phys. B 31, 1650251 (2017)

    Article  ADS  Google Scholar 

  31. S. Rakshit, A. Ray, B.K. Bera, D. Ghosh, Nonlinear Dynam. 94, 785 (2018)

    Article  Google Scholar 

  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. Z. Wei, F. Parastesh, H. Azarnoush, S. Jafari, D. Ghosh, M. Perc, M. Slavinec, Europhys. Lett. 123, 48003 (2018)

    Article  Google Scholar 

  34. A. Schmidt, T. Kasimatis, J. Hizanidis, A. Provata, P. Hövel, Phys. Rev. E 95, 032224 (2017)

    MathSciNet  Article  ADS  Google Scholar 

  35. I. Omelchenko, A. Provata, J. Hizanidis, E. Schöll, P. Hövel, Phys. Rev. E 91, 022917 (2015)

    MathSciNet  Article  ADS  Google Scholar 

  36. J.M. Sausedo-Solorio, A.N. Pisarchik, Eur. Phys. J. Special Topics 226, 1911 (2017)

    Article  ADS  Google Scholar 

  37. J.L. Wang, H.N. Wu, T. Huang, Automatica 56, 105 (2015)

    Article  Google Scholar 

  38. Z. Levnajić, B. Tadić, J. Stat. Mech. Theory Exp. 3, P03003 (2018)

    Google Scholar 

  39. H. Gu, Z. Zhao, PloS One 10, e0138593 (2015)

    Article  Google Scholar 

  40. Y. Çakir, Turk. J. Electr. Eng. Comp. Sci. 25, 2595 (2017)

    Article  Google Scholar 

  41. E. Rossoni, Y. Chen, M. Ding, J. Feng, Phys. Rev. E 71, 061904 (2005)

    MathSciNet  Article  ADS  Google Scholar 

  42. M. Masoliver, N. Malik, E. Schöll, A. Zakharova, Chaos 27, 101102 (2017)

    MathSciNet  Article  ADS  Google Scholar 

  43. M. Jalili, Neurocomputing 74, 1551 (2011)

    Article  Google Scholar 

  44. M. Jalili, Chaos 23, 013146 (2013)

    MathSciNet  Article  ADS  Google Scholar 

  45. A. Zakharova, N. Semenova, V. Anishchenko, E. Schöll, Chaos 27, 114320 (2017)

    MathSciNet  Article  ADS  Google Scholar 

  46. A. Gjurchinovski, E. Schöll, A. Zakharova, Phys. Rev. E 95, 042218 (2017)

    MathSciNet  Article  ADS  Google Scholar 

  47. S. Nobukawa, H. Nishimura, T. Yamanishi, Sci. Rep. 7, 1331 (2017)

    Article  ADS  Google Scholar 

  48. Y. Hao, Y. Gong, L. Wang, X. Ma, C. Yang, Chaos Soliton. Fract. 44, 260 (2011)

    Article  ADS  Google Scholar 

  49. M.V. Bennett, R.S. Zukin, Neuron 41, 495 (2004)

    Article  Google Scholar 

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Correspondence to Matjaž Perc.

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Shafiei, M., Parastesh, F., Jalili, M. et al. Effects of partial time delays on synchronization patterns in Izhikevich neuronal networks. Eur. Phys. J. B 92, 36 (2019). https://doi.org/10.1140/epjb/e2018-90638-x

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  • DOI: https://doi.org/10.1140/epjb/e2018-90638-x

Keywords

  • Statistical and Nonlinear Physics