On Chaotic Subthreshold Oscillations in a Simple Neuronal Model

M. Zaks

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 6, Issue: 1, page 149-162
  • ISSN: 0973-5348

Abstract

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In a simple FitzHugh-Nagumo neuronal model with one fast and two slow variables, a sequence of period-doubling bifurcations for small-scale oscillations precedes the transition into the spiking regime. For a wide range of values of the timescale separation parameter, this scenario is recovered numerically. Its relation to the singularly perturbed integrable system is discussed.

How to cite

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Zaks, M.. "On Chaotic Subthreshold Oscillations in a Simple Neuronal Model." Mathematical Modelling of Natural Phenomena 6.1 (2010): 149-162. <http://eudml.org/doc/197663>.

@article{Zaks2010,
abstract = {In a simple FitzHugh-Nagumo neuronal model with one fast and two slow variables, a sequence of period-doubling bifurcations for small-scale oscillations precedes the transition into the spiking regime. For a wide range of values of the timescale separation parameter, this scenario is recovered numerically. Its relation to the singularly perturbed integrable system is discussed.},
author = {Zaks, M.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {slow-fast equations; period-doubling bifurcation},
language = {eng},
month = {6},
number = {1},
pages = {149-162},
publisher = {EDP Sciences},
title = {On Chaotic Subthreshold Oscillations in a Simple Neuronal Model},
url = {http://eudml.org/doc/197663},
volume = {6},
year = {2010},
}

TY - JOUR
AU - Zaks, M.
TI - On Chaotic Subthreshold Oscillations in a Simple Neuronal Model
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/6//
PB - EDP Sciences
VL - 6
IS - 1
SP - 149
EP - 162
AB - In a simple FitzHugh-Nagumo neuronal model with one fast and two slow variables, a sequence of period-doubling bifurcations for small-scale oscillations precedes the transition into the spiking regime. For a wide range of values of the timescale separation parameter, this scenario is recovered numerically. Its relation to the singularly perturbed integrable system is discussed.
LA - eng
KW - slow-fast equations; period-doubling bifurcation
UR - http://eudml.org/doc/197663
ER -

References

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