Generation of slow phase-locked oscillation and variability of the interspike intervals in globally coupled neuronal oscillators
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1.
Graduate School of Engineering, Kyoto University, Kyoto 615-8510
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2.
Faculty of Human Relation, Kyoto Koka Women's University, Kyoto 615-0882
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Received:
01 December 2012
Accepted:
29 June 2018
Published:
01 September 2013
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MSC :
Primary: 92C20, 34C15; Secondary: 37N25.
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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.
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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Abstract
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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