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Synchronization with an arbitrary phase shift in a pair of synaptically coupled neural oscillators

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Abstract

The phase dynamics of a pair of spiking neural oscillators coupled by a unidirectional nonlinear connection has been studied. The synchronization effect with the controlled relative phase of spikes has been obtained for various coupling strengths and depolarization parameters. It has been found that the phase value is determined by the difference between the depolarization levels of neurons and is independent of the synaptic coupling strength. The synchronization mechanism has been studied by means of the construction and analysis of one-dimensional phase maps. The phase locking effect for spikes has been interpreted in application to the synaptic plasticity in neurobiology.

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References

  1. A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences, Cambridge Nonlinear Science Series, 1st ed. (Cambridge Univ. Press, Cambridge, 2003).

    Google Scholar 

  2. E. M. Izhikevich, Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting (The MIT Press, MA, 2007).

    Google Scholar 

  3. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer, Heidelberg, 1984).

    Book  MATH  Google Scholar 

  4. R. R. Llinás, I of the Vortex: From Neurons to Self (MIT Press, London, 2002).

    Google Scholar 

  5. G. Buzsáki, Rhythms of the Brain (Oxford Univ. Press, New York, 2006).

    Book  MATH  Google Scholar 

  6. G. Buzsáki and J. J. Chrobak, Curr. Opin. Neurobiol. 5, 504 (1995).

    Article  Google Scholar 

  7. J. Csicsvari, H. Hirase, A. Mamiya, and G. Buzsáki, Neuron 28, 585 (2000).

    Article  Google Scholar 

  8. C. S. Rex, L. L. Colgin, Y. Jia, M. Casale, T. K. Yanagi- hara, M. Debenedetti, C. M. Gall, E. A. Kramar, and G. Lynch, PloS one 4(11), e7761 (2009).

    Article  ADS  Google Scholar 

  9. R. S. Fisher, W. van Emde Boas, W. Blume, C. Elger, P. Genton, P. Lee, and J. Engel, Epilepsia 46, 470 (2005).

    Article  Google Scholar 

  10. H. Markram, J. Lübke, M. Frotscher, and B. Sakmann, Science 275(5297), 213 (1997).

    Article  Google Scholar 

  11. G. Q. Bi and M. M. Poo, J. Neurosci. 18, 10464 (1998).

    Google Scholar 

  12. V. Kazantsev and I. Tyukin, PloS one 7, e30411 (2012).

    Article  ADS  MathSciNet  Google Scholar 

  13. G. B. Ermentrout and N. Kopell, SIAM J. Appl. Math. 50, 125 (1990).

    Article  MATH  MathSciNet  Google Scholar 

  14. G. B. Ermentrout and N. Kopell, J. Math. Biol. 29, 195 (1991).

    Article  MATH  MathSciNet  Google Scholar 

  15. D. Hansel, G. Mato, and C. Meunier, Europhys. Lett. 23, 367 (1993).

    Article  ADS  Google Scholar 

  16. D. Hansel, G. Mato, and C. Meunier, Neural Comput. 7, 307 (1995).

    Article  Google Scholar 

  17. G. B. Ermentrout, L. Glass, and B. E. Oldeman, Neural Comput. 24, 3111 (2012).

    Article  MATH  MathSciNet  Google Scholar 

  18. E. Izhikevich and Y. Kuramoto, in Encyclopedia of Mathematical Physics (2006), p. 48.

    Google Scholar 

  19. A. Semyanov, Neurochem. Int. 52, 31 (2008).

    Article  Google Scholar 

  20. A. Dityatev and M. Schachner, Nature Rev. Neurosci. 4, 456 (2003).

    Article  Google Scholar 

  21. A. Dityatev and D. Rusakov, Curr. Opin. Neurobiol. 21, 353 (2011).

    Article  Google Scholar 

  22. S. Gordleeva, S. Stasenko, A. Semyanov, A. Dityatev, and V. Kazantsev, Frontiers in Comput. Neurosci. 6, 1 (2012).

    Article  Google Scholar 

  23. M. Ciszak, O. Calvo, C. Masoller, C. Mirasso, and R. Toral, Phys. Rev. Lett. 90, 204102 (2003).

    Article  ADS  Google Scholar 

  24. H. Voss, Phys. Rev. E 61, 5115 (2000).

    Article  ADS  Google Scholar 

  25. A. L. Hodgkin and A. F. Huxley, J. Physiol. 117, 500 (1952).

    Google Scholar 

  26. L. S. Borkowski, Nonlinear Dynamics of Hodgkin-Huxley Neurons (Adam Mickiewicz Univ. Press, Poznan, 2010).

    Google Scholar 

  27. J. Rinzel and R. N. Miller, Math. Biosci. 49, 27 (1980).

    Article  MATH  MathSciNet  Google Scholar 

  28. V. Kazantsev and S. Asatryan, Phys. Rev. E 84, 031913 (2011).

    Article  ADS  Google Scholar 

  29. V. B. Kazantsev, V. I. Nekorkin, S. Binczak, S. Jacquir, and J. M. Bilbault, Chaos (Woodbury, N.Y.) 15, 23103 (2005).

    Article  MathSciNet  Google Scholar 

  30. P. F. Rowat and A. I. Selverston, J. Neurophysiol. 70, 1030 (1993).

    Google Scholar 

  31. V. Kazantsev and A. Pimashkin, Phys. Rev. E: Stat. Nonlin. Soft Matter Phys. 76, 031912 (2007).

    Article  ADS  Google Scholar 

  32. A. Simonov, I. Kastalskiy, and V. Kazantsev, Neural Networks 33, 67 (2012).

    Article  Google Scholar 

  33. D. H. Perkel, J. H. Schulman, T. H. Bullock, G. P. Moore, and J. P. Segundo, Science 145(3627), 61 (1964).

    Article  ADS  Google Scholar 

  34. T. I. Netoff, C. D. Acker, J. C. Bettencourt, and J. A. White, J. Comput. Neurosci. 18, 287 (2005).

    Article  Google Scholar 

  35. P. Goel and B. Ermentrout, Phys. D: Nonlin. Phenom. 163, 191 (2002).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  36. M. R. Guevara, A. Shrier, and L. Glass, Am. J. Physiol. Heart Circ. Physiol. 251, H1298 (1986).

    Google Scholar 

  37. A. D. Reyes and E. E. Fetz, J. Neurophysiol. 69, 1661 (1993).

    Google Scholar 

  38. F. S. Matias, P. V. Carelli, C. R. Mirasso, and M. Copelli, Phys. Rev. E 84, 021922 (2011).

    Article  ADS  Google Scholar 

  39. C. Mayol, C. R. Mirasso, and R. Toral, Phys. Rev. E 85, 056216 (2012).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Lobachevsky State University of Nizhni Novgorod, pr. Gagarina 23, Nizhni Novgorod, 603950, Russia

    A. Yu. Simonov, S. Yu. Gordleeva & V. B. Kazantsev

  2. Centro de Investigaciones en Óptica, 37150, León, Guanajuato, México

    A. N. Pisarchik

  3. Centro de Tecnologiá Biomédica, Universidad Politécnica de Madrid, Pozuelo de Alarcón, 28223, Madrid, Spain

    A. N. Pisarchik

  4. Institute of Applied Physics, Russian Academy of Sciences, ul. Ul’yanova 46, Nizhni Novgorod, 603950, Russia

    S. Yu. Gordleeva & V. B. Kazantsev

Authors
  1. A. Yu. Simonov
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  2. S. Yu. Gordleeva
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  3. A. N. Pisarchik
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  4. V. B. Kazantsev
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Correspondence to A. Yu. Simonov.

Additional information

Original Russian Text © A.Yu. Simonov, S.Yu. Gordleeva, A.N. Pisarchik, V.B. Kazantsev, 2013, published in Pis’ma v Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2013, Vol. 98, No. 10, pp. 707–712.

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Simonov, A.Y., Gordleeva, S.Y., Pisarchik, A.N. et al. Synchronization with an arbitrary phase shift in a pair of synaptically coupled neural oscillators. Jetp Lett. 98, 632–637 (2014). https://doi.org/10.1134/S0021364013230136

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  • DOI: https://doi.org/10.1134/S0021364013230136

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