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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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  • © 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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