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Mathematical Biosciences and Engineering

2014, Volume 11, Issue 1: 125-138. doi: 10.3934/mbe.2014.11.125
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Generation of slow phase-locked oscillation and variability of the interspike intervals in globally coupled neuronal oscillators

  • 1.
    Graduate School of Engineering, Kyoto University, Kyoto 615-8510
  • 2.
    Faculty of Human Relation, Kyoto Koka Women's University, Kyoto 615-0882
  • Received: 01 December 2012 Accepted: 29 June 2018 Published: 01 September 2013

  • MSC : Primary: 92C20, 34C15; Secondary: 37N25.

  • To elucidate how a biological rhythm is regulated,the extended (three-dimensional) Bonhoeffer-van der Pol or FitzHugh-Nagumo equations are employed toinvestigate the dynamics of a population of neuronal oscillators globally coupled through a common buffer (mean field).Interesting phenomena, such as extraordinarily slow phase-locked oscillations (compared to the natural period of each neuronal oscillator)and the death of all oscillations, are observed.We demonstrate that the slow synchronization is due mainly to the existence of ``fast" oscillators.Additionally, we examine the effect of noise on the synchronization and variability of the interspike intervals.Peculiar phenomena, such as noise-induced acceleration and deceleration, are observed.The results herein suggest that very small noise may significantly influence a biological rhythm.

    Citation: Ryotaro Tsuneki, Shinji Doi, Junko Inoue. Generation of slow phase-locked oscillation and variability of the interspike intervals in globally coupled neuronal oscillators[J]. Mathematical Biosciences and Engineering, 2014, 11(1): 125-138. doi: 10.3934/mbe.2014.11.125

    Related Papers:

  • To elucidate how a biological rhythm is regulated,the extended (three-dimensional) Bonhoeffer-van der Pol or FitzHugh-Nagumo equations are employed toinvestigate the dynamics of a population of neuronal oscillators globally coupled through a common buffer (mean field).Interesting phenomena, such as extraordinarily slow phase-locked oscillations (compared to the natural period of each neuronal oscillator)and the death of all oscillations, are observed.We demonstrate that the slow synchronization is due mainly to the existence of ``fast" oscillators.Additionally, we examine the effect of noise on the synchronization and variability of the interspike intervals.Peculiar phenomena, such as noise-induced acceleration and deceleration, are observed.The results herein suggest that very small noise may significantly influence a biological rhythm.


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    [1] Biol. Cybern., 100 (2009), 491-504.
    [2] Physica D, 240 (2011), 719-731.
    [3] Phys. Rev. Lett., 87 (2001), 048101.
    [4] Concordia University, 2009.
    [5] AIP Conf. Proc., 1339 (2011), 210-221.
    [6] J. Comp. Neurosci., 19 (2005), 325-356.
    [7] J. Math. Biol., 26 (1988), 435-454.
    [8] SIAM J. Appl. Dyn. Syst., 8 (2009), 253-278.
    [9] Biophy. J., 1 (1961), 445-466.
    [10] Nature, 410 (2001), 277-284.
    [11] Neural Comput., 10 (1998), 1047-1065.
    [12] Naturwiss., 96 (2009), 1091-1097.
    [13] J. Physiol., 117 (1952), 500-544.
    [14] Bull. Math. Biol., 47 (1985), 1-21.
    [15] Physica D, 237 (2008), 2933-2944.
    [16] J. Theor. Biol., 297 (2012), 61-72.
    [17] Springer Series in Synergetics, 19, Springer-Verlag, Berlin, 1984.
    [18] Neural Comput., 15 (2003), 1761-1788.
    [19] Proc. IRE, 50 (1962), 2061-2070.
    [20] Cambridge Nonlinear Science Series, 12, Cambridge University Press, Cambridge, 2001.
    [21] Proc. of AROB 7th '02, (2002), 54-57.
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  • © 2014 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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