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:
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
Related Papers:
[1] |
P. E. Greenwood, L. M. Ward .
Rapidly forming, slowly evolving, spatial patterns from quasi-cycle Mexican Hat coupling. Mathematical Biosciences and Engineering, 2019, 16(6): 6769-6793.
doi: 10.3934/mbe.2019338
|
[2] |
Shinsuke Koyama, Lubomir Kostal .
The effect of interspike interval statistics on the information gainunder the rate coding hypothesis. Mathematical Biosciences and Engineering, 2014, 11(1): 63-80.
doi: 10.3934/mbe.2014.11.63
|
[3] |
Rakesh Pilkar, Erik M. Bollt, Charles Robinson .
Empirical mode decomposition/Hilbert transform analysis of postural responses to small amplitude anterior-posterior sinusoidal translations of varying frequencies. Mathematical Biosciences and Engineering, 2011, 8(4): 1085-1097.
doi: 10.3934/mbe.2011.8.1085
|
[4] |
Sven Blankenburg, Benjamin Lindner .
The effect of positive interspike interval correlations on neuronal information transmission. Mathematical Biosciences and Engineering, 2016, 13(3): 461-481.
doi: 10.3934/mbe.2016001
|
[5] |
Hwayeon Ryu, Sue Ann Campbell .
Stability, bifurcation and phase-locking of time-delayed excitatory-inhibitory neural networks. Mathematical Biosciences and Engineering, 2020, 17(6): 7931-7957.
doi: 10.3934/mbe.2020403
|
[6] |
Alan Dyson .
Traveling wave solutions to a neural field model with oscillatory synaptic coupling types. Mathematical Biosciences and Engineering, 2019, 16(2): 727-758.
doi: 10.3934/mbe.2019035
|
[7] |
Changgui Gu, Ping Wang, Tongfeng Weng, Huijie Yang, Jos Rohling .
Heterogeneity of neuronal properties determines the collective behavior of the neurons in the suprachiasmatic nucleus. Mathematical Biosciences and Engineering, 2019, 16(4): 1893-1913.
doi: 10.3934/mbe.2019092
|
[8] |
Roberta Sirovich, Laura Sacerdote, Alessandro E. P. Villa .
Cooperative behavior in a jump diffusion model for a simple network of spiking neurons. Mathematical Biosciences and Engineering, 2014, 11(2): 385-401.
doi: 10.3934/mbe.2014.11.385
|
[9] |
Xiao Wu, Shuying Lu, Feng Xie .
Relaxation oscillations of a piecewise-smooth slow-fast Bazykin's model with Holling type Ⅰ functional response. Mathematical Biosciences and Engineering, 2023, 20(10): 17608-17624.
doi: 10.3934/mbe.2023782
|
[10] |
Virginia Giorno, Serena Spina .
On the return process with refractoriness for a non-homogeneous Ornstein-Uhlenbeck neuronal model. Mathematical Biosciences and Engineering, 2014, 11(2): 285-302.
doi: 10.3934/mbe.2014.11.285
|
-
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.
References
[1]
|
Biol. Cybern., 100 (2009), 491-504.
|
[2]
|
Physica D, 240 (2011), 719-731.
|
[3]
|
Phys. Rev. Lett., 87 (2001), 048101.
|
[4]
|
Concordia University, 2009.
|
[5]
|
AIP Conf. Proc., 1339 (2011), 210-221.
|
[6]
|
J. Comp. Neurosci., 19 (2005), 325-356.
|
[7]
|
J. Math. Biol., 26 (1988), 435-454.
|
[8]
|
SIAM J. Appl. Dyn. Syst., 8 (2009), 253-278.
|
[9]
|
Biophy. J., 1 (1961), 445-466.
|
[10]
|
Nature, 410 (2001), 277-284.
|
[11]
|
Neural Comput., 10 (1998), 1047-1065.
|
[12]
|
Naturwiss., 96 (2009), 1091-1097.
|
[13]
|
J. Physiol., 117 (1952), 500-544.
|
[14]
|
Bull. Math. Biol., 47 (1985), 1-21.
|
[15]
|
Physica D, 237 (2008), 2933-2944.
|
[16]
|
J. Theor. Biol., 297 (2012), 61-72.
|
[17]
|
Springer Series in Synergetics, 19, Springer-Verlag, Berlin, 1984.
|
[18]
|
Neural Comput., 15 (2003), 1761-1788.
|
[19]
|
Proc. IRE, 50 (1962), 2061-2070.
|
[20]
|
Cambridge Nonlinear Science Series, 12, Cambridge University Press, Cambridge, 2001.
|
[21]
|
Proc. of AROB 7th '02, (2002), 54-57.
|
-
-
This article has been cited by:
1.
|
Ryuto Okubo, Shunto Kawae, Shinji Doi,
Analysis of differentiation ratio regulation dynamics in a globally coupled cell population model based on its reduced models,
2025,
16,
2185-4106,
168,
10.1587/nolta.16.168
|
|
-
-