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Mutual and intermittent enhancements of synchronization transitions by autaptic and synaptic delay in scale-free neuron networks

  • Qi Wang
  • Yubing GongEmail author
  • Huijuan Xie
Regular Article

Abstract

In neural networks, there exist both synaptic delays among different neurons and autaptic self-feedback delays in a neuron itself. In this paper, we study synchronization transitions induced by synaptic and autaptic delays in scale-free neuron networks, mainly exploring how these two time delays affect synchronization transitions induced by each other. It is found that the synchronization transitions induced by synaptic (autaptic) delay are intermittently enhanced when autaptic (synaptic) delay is varied. There are optimal autaptic strength and synaptic coupling strength by which the synchronization transitions induced by autaptic and synaptic delays become strongest. The underlying mechanisms are briefly discussed in terms of the relationships of autaptic delay, synaptic delay, and inter-burst interval. These results show that synaptic and autaptic delays could contribute to each other and enhance synchronization transitions in the neuronal networks. This implies that autaptic and synaptic delays could play a vital role for the information transmission in neural systems.

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    R. Salvador, J. Suckling, M.R. Coleman, J.D. Pickard, D. Menon, E. Bullmore, Cereb. Cortex 15, 1332 (2005) CrossRefGoogle Scholar
  2. 2.
    S.D. Bassett, T.E. Bullmore, Neuroscientist 12, 512 (2006)CrossRefGoogle Scholar
  3. 3.
    V.M. Eguíluz, D.R. Chialvo, G.A. Cecchi, M. Baliki, A.V. Apkarian, Phys Rev Lett 94, 018102 (2005) ADSCrossRefGoogle Scholar
  4. 4.
    M. Kaiser, R. Martin, P. Andras, M.P. Young, Eur. J. Neurosci. 25, 3185 (2007) CrossRefGoogle Scholar
  5. 5.
    E. Kandel, J. Schwartz, T. Jessell, Principles of Neural Science (Elsevier, Amsterdam, 1991)Google Scholar
  6. 6.
    M.D. Mann, The Nervous System and Behavior: An Introduction (Harper and Row, Maryland, 1981)Google Scholar
  7. 7.
    E.M. Izhikevich, Neural Comput. 18, 245 (2006)MathSciNetCrossRefGoogle Scholar
  8. 8.
    H. Van der Loos, E.M. Glaser, Brain Res. 48, 355 (1972)CrossRefGoogle Scholar
  9. 9.
    J. Lübke, H. Markram, M. Frotscher, B. Sakmann, J. Neurosci. 16, 3209 (1996) Google Scholar
  10. 10.
    J.M. Bekkers, Curr. Biol. 8, R52 (1998)CrossRefGoogle Scholar
  11. 11.
    J.M. Bekkers, Curr. Biol. 13, R433 (2003) CrossRefGoogle Scholar
  12. 12.
    M.H. Flight, Nat. Rev. Neurosci. 10, 316 (2009)Google Scholar
  13. 13.
    T. Branco, K. Staras, Nat. Rev. Neurosci. 10, 373 (2009)CrossRefGoogle Scholar
  14. 14.
    C. Wyart, S. Cocco, L. Bourdieu, J.F. Leger, C. Herr, D. Chatenay, J. Neuro. Physiol. 93, 3370 (2005) Google Scholar
  15. 15.
    A. Bacci, J.R. Huguenard, Neuron 49, 119 (2006)CrossRefGoogle Scholar
  16. 16.
    K. Ikeda, J.M. Bekkers, Curr. Biol. 16, R308 (2006) CrossRefGoogle Scholar
  17. 17.
    O.V. Popovych, C. Hauptmann, P.A. Tass, Biol. Cybern. 95, 69 (2006)MathSciNetCrossRefGoogle Scholar
  18. 18.
    T. Prager, H.P. Lerch, L. Schimansky-Geier, E. Schoell, J. Phys. A 40, 11045 (2007) ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    R. Saada, N. Miller, I. Hurwitz, A.J. Susswein, Curr. Biol. 19, 479 (2009)CrossRefGoogle Scholar
  20. 20.
    Y. Li, G. Schmid, P. Hänggi, L. Schimansky-Geier, Phys. Rev. E 82, 061907 (2010) ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    C.G. Rusin, S.E. Johnson, J. Kapur, J.L. Hudson, Phys. Rev. E 84, 066202 (2011) ADSCrossRefGoogle Scholar
  22. 22.
    M. Hashemi, A. Valizadeh, Y. Azizi, Phys. Rev. E 85, 021917 (2012) ADSCrossRefGoogle Scholar
  23. 23.
    H.T. Wang, J. Ma, Y.L. Chen, Y. Chen, Commun. Nonlinear Sci. Numer. Simul. 19, 3242 (2014) ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    H.T. Wang, L.F. Wang, Y.L. Chen, Y. Chen, Chaos 24, 033122 (2014) ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    H.X. Qin, J. Ma, W.Y. Jin, C.N. Wang, Sci. China Tech. Sci. 57, 936 (2014)CrossRefGoogle Scholar
  26. 26.
    H.X. Qin, J. Ma, C.N. Wang, R.T. Chu, Sci. China Phys. Mech. Astron. 57, 1918 (2014) ADSCrossRefGoogle Scholar
  27. 27.
    C.M. Gray, W. Singer, Proc. Natl. Acad. Sci. USA 86, 1698 (1989) ADSCrossRefGoogle Scholar
  28. 28.
    M. Bazhenov, M. Stopfer, M. Rabinovich, R. Huerta, H.D.I. Abarbanel, Y.J. Sejnowski, G. Laurent, Neuron 30, 553 (2001)CrossRefGoogle Scholar
  29. 29.
    M.R. Mehta, A.K. Lee, M.A. Wilson, Nature 417, 741 (2001) ADSCrossRefGoogle Scholar
  30. 30.
    R. Levy, W.D. Hutchison, A.M. Lozano, J.O. Dostrovsky, J. Neurosci. 20, 7766 (2000) Google Scholar
  31. 31.
    F. Mormann, T. Kreuz, R.G. Andrzejak, P. David, K. Lehnertz, C.E. Elger, Epilepsy Res. 53, 173 (2003)CrossRefGoogle Scholar
  32. 32.
    A. Arenas, A. Díaz-Guilera, J. Kurths, Y. Moreno, C.S. Zhou, Phys. Rep. 469, 93 (2008)ADSMathSciNetCrossRefGoogle Scholar
  33. 33.
    J.A.K. Suykens, G.V. Osipov, Chaos 18, 037101 (2008) ADSCrossRefGoogle Scholar
  34. 34.
    Q.Y. Wang, Q.S. Lu, G.R. Chen, Int. J. Bifurc. Chaos 18, 1189 (2008) MathSciNetCrossRefGoogle Scholar
  35. 35.
    Q.Y. Wang, Z.S. Duan, M. Perc, G.R. Chen, Europhys. Lett. 83, 50008 (2008) ADSCrossRefGoogle Scholar
  36. 36.
    Q.Y. Wang, M. Perc, Z.S. Duan, G.R. Chen, Phys. Rev. E 80, 026206 (2009) ADSCrossRefGoogle Scholar
  37. 37.
    Q.Y. Wang, M. Perc, Z.S. Duan, G.R. Chen, Physica A 389, 3299 (2010) ADSCrossRefGoogle Scholar
  38. 38.
    Q.Y. Wang, G.R. Chen, M. Perc, PLoS ONE 6, e15851 (2011) ADSCrossRefGoogle Scholar
  39. 39.
    D.Q. Guo, Q.Y. Wang, M. Perc, Phys. Rev. E 85, 061905 (2012) ADSCrossRefGoogle Scholar
  40. 40.
    Y. Qian, Y.R. Zhao, F. Liu, X.D. Huang, Z.Y. Zhang, Y.Y. Mi, Commun. Nonlinear. Sci. Numer. Simulat. 18, 3509 (2013) ADSMathSciNetCrossRefGoogle Scholar
  41. 41.
    Y.H. Hao, Y.B. Gong, L. Wang, X.G. Ma, C.L. Yang, Chaos Solitons Fractals 44, 260 (2011)ADSMathSciNetCrossRefGoogle Scholar
  42. 42.
    B. Xu, Y.B. Gong, L. Wang, Y.N. Wu, Nonlin. Dyn. 72, 79 (2013)MathSciNetCrossRefGoogle Scholar
  43. 43.
    X.J. Sun, J.Z. Lei, M. Perc, J. Kurths, G.R. Chen, Chaos 21, 016110 (2011) ADSCrossRefGoogle Scholar
  44. 44.
    Y.N. Wu, Y.B. Gong, Q. Wang, Eur. Phys. J. B 87, 198 (2014)ADSMathSciNetCrossRefGoogle Scholar
  45. 45.
    Y.N. Wu, Y.B. Gong, Q. Wang, Physica A 421, 347 (2015) ADSCrossRefGoogle Scholar
  46. 46.
    Y.N. Wu, Y.B. Gong, Q. Wang, Chaos 25, 043113 (2015) ADSMathSciNetCrossRefGoogle Scholar
  47. 47.
    Q. Wang, Y.B. Gong, Y.N. Wu, Eur. Phys. J. B 88, 103 (2015)ADSCrossRefGoogle Scholar
  48. 48.
    H.A. Braun, M.T. Huber, M. Dewald, K. Schafer, K. Voigt, Int. J. Bifurcat. Chaos 8, 881 (1998)CrossRefGoogle Scholar
  49. 49.
    H.A. Braun, H. Wissing, K. Schäfer, M.C. Hirsch, Nature 367, 270 (1994) ADSCrossRefGoogle Scholar
  50. 50.
    H.A. Braun, K. Schäfer, K. Voigt, R. Peters, F. Bretschneider, X. Pei, J. Comput. Neurosci. 4, 335 (1997)CrossRefGoogle Scholar
  51. 51.
    H.A. Braun, M. Dewald, K. Schäfer, K. Voigt, X. Pei, K. Dolan, J. Comput. Neurosci. 7, 17 (1999)CrossRefGoogle Scholar
  52. 52.
    U. Feudel, A. Neiman, X. Pei, W. Wojtenek, H.A. Braun, M. Huber, F. Moss, Chaos 10, 231 (2000)ADSMathSciNetCrossRefGoogle Scholar
  53. 53.
    W. Braun, B. Eckhardt, H.A. Braun, M. Huber, Phys. Rev. E 62, 6352 (2000) ADSCrossRefGoogle Scholar
  54. 54.
    C. Masoller, M.C. Torrent, J. García-Ojalvo, Phys. Rev. E 78, 041907 (2008) ADSCrossRefGoogle Scholar
  55. 55.
    A.-L. Barabási, R. Albert, Science 286, 509 (1999) ADSMathSciNetCrossRefGoogle Scholar
  56. 56.
    A. Destexhe, Z.F. Mainen, T.J. Sejnowski, Neural. Comput. 6, 14 (1994)CrossRefGoogle Scholar
  57. 57.
    N. Burić, K. Todorović, N. Vasović, Phys. Rev. E 78, 036211 (2008) ADSCrossRefGoogle Scholar
  58. 58.
    Y.B. Gong, B. Xu, Q. Xu, C.L. Yang, T.Q. Ren, Z.H. Hou, H.W. Xin, Phys. Rev. E 73, 046137 (2006) ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.School of Physics and Optoelectronic Engineering, Ludong UniversityShandongP.R. China

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