Generation of slow phase-locked oscillation and variability of the interspike intervals in globally coupled neuronal oscillators

  • 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

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  • 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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