# American Institute of Mathematical Sciences

2014, 11(1): 125-138. doi: 10.3934/mbe.2014.11.125

## 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, Japan, Japan 2 Faculty of Human Relation, Kyoto Koka Women's University, Kyoto 615-0882, Japan

Received  December 2012 Revised  July 2013 Published  September 2013

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.
Citation: 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 & Engineering, 2014, 11 (1) : 125-138. doi: 10.3934/mbe.2014.11.125
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