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

Ryotaro Tsuneki; Shinji Doi; Junko Inoue

doi:10.3934/mbe.2014.11.125

Article Contents

2014, Volume 11, Issue 1: 125-138. Doi: 10.3934/mbe.2014.11.125 open access

This issue Previous Article Fano factor estimation Next Article Structural phase transitions in neural networks

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: November 30, 2012

Revised: June 30, 2013

Published: August 2013

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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 to investigate 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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Mathematics Subject Classification: Primary: 92C20, 34C15; Secondary: 37N25.

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