Generation of slow phase-locked oscillation and variability of the interspike intervals in globally coupled neuronal oscillators
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...
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AIMS Press
2013-08-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.125 |
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| author | Ryotaro Tsuneki Shinji Doi Junko Inoue |
| author_facet | Ryotaro Tsuneki Shinji Doi Junko Inoue |
| author_sort | Ryotaro Tsuneki |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-de528793070844cdb53b1378c31fc699 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-08-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-de528793070844cdb53b1378c31fc6992025-01-24T02:26:48ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-08-0111112513810.3934/mbe.2014.11.125Generation of slow phase-locked oscillation and variability of the interspike intervals in globally coupled neuronal oscillatorsRyotaro Tsuneki0Shinji Doi1Junko Inoue2Graduate School of Engineering, Kyoto University, Kyoto 615-8510Graduate School of Engineering, Kyoto University, Kyoto 615-8510Faculty of Human Relation, Kyoto Koka Women's University, Kyoto 615-0882To 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.https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.125globally coupled systemslow phase-locked oscillationinterspike interval.neuronal oscillator |
| spellingShingle | Ryotaro Tsuneki Shinji Doi Junko Inoue Generation of slow phase-locked oscillation and variability of the interspike intervals in globally coupled neuronal oscillators Mathematical Biosciences and Engineering globally coupled system slow phase-locked oscillation interspike interval. neuronal oscillator |
| title | Generation of slow phase-locked oscillation and variability of the interspike intervals in globally coupled neuronal oscillators |
| title_full | Generation of slow phase-locked oscillation and variability of the interspike intervals in globally coupled neuronal oscillators |
| title_fullStr | Generation of slow phase-locked oscillation and variability of the interspike intervals in globally coupled neuronal oscillators |
| title_full_unstemmed | Generation of slow phase-locked oscillation and variability of the interspike intervals in globally coupled neuronal oscillators |
| title_short | Generation of slow phase-locked oscillation and variability of the interspike intervals in globally coupled neuronal oscillators |
| title_sort | generation of slow phase locked oscillation and variability of the interspike intervals in globally coupled neuronal oscillators |
| topic | globally coupled system slow phase-locked oscillation interspike interval. neuronal oscillator |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.125 |
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