Bifurcation of a Modified BVP Circuit Model for Neurons Generating Rectangular Waves
Summary :
We investigate bifurcations of burst oscillations with rectangular waveform observed in a modified Bonhöffer-van der Pol equation, which is considered as a circuit model for neurons of a feeding rhythm generator. In particular, we clarify a mechanism of properties in a one-parameter graph on the period of oscillations, showing a staircase with hysteresis jumps, by studying a successive bifurcation process including a chain of homoclinic bifurcations. The occurrence of homoclinic bifurcations is confirmed by using the linking number of limit cycles related with the stable manifold through an equilibrium.
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- IEICE TRANSACTIONS on Fundamentals Vol.E82-A No.9 pp.1729-1736
- Publication Date
- 1999/09/25
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- Special Section PAPER (Special Section on Nonlinear Theory and Its Applications)
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Kunichika TSUMOTO, Tetsuya YOSHINAGA, Hiroshi KAWAKAMI, "Bifurcation of a Modified BVP Circuit Model for Neurons Generating Rectangular Waves" in IEICE TRANSACTIONS on Fundamentals,
vol. E82-A, no. 9, pp. 1729-1736, September 1999, doi: .
Abstract: We investigate bifurcations of burst oscillations with rectangular waveform observed in a modified Bonhöffer-van der Pol equation, which is considered as a circuit model for neurons of a feeding rhythm generator. In particular, we clarify a mechanism of properties in a one-parameter graph on the period of oscillations, showing a staircase with hysteresis jumps, by studying a successive bifurcation process including a chain of homoclinic bifurcations. The occurrence of homoclinic bifurcations is confirmed by using the linking number of limit cycles related with the stable manifold through an equilibrium.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e82-a_9_1729/_p
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@ARTICLE{e82-a_9_1729,
author={Kunichika TSUMOTO, Tetsuya YOSHINAGA, Hiroshi KAWAKAMI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Bifurcation of a Modified BVP Circuit Model for Neurons Generating Rectangular Waves},
year={1999},
volume={E82-A},
number={9},
pages={1729-1736},
abstract={We investigate bifurcations of burst oscillations with rectangular waveform observed in a modified Bonhöffer-van der Pol equation, which is considered as a circuit model for neurons of a feeding rhythm generator. In particular, we clarify a mechanism of properties in a one-parameter graph on the period of oscillations, showing a staircase with hysteresis jumps, by studying a successive bifurcation process including a chain of homoclinic bifurcations. The occurrence of homoclinic bifurcations is confirmed by using the linking number of limit cycles related with the stable manifold through an equilibrium.},
keywords={},
doi={},
ISSN={},
month={September},}
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TY - JOUR
TI - Bifurcation of a Modified BVP Circuit Model for Neurons Generating Rectangular Waves
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1729
EP - 1736
AU - Kunichika TSUMOTO
AU - Tetsuya YOSHINAGA
AU - Hiroshi KAWAKAMI
PY - 1999
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E82-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 1999
AB - We investigate bifurcations of burst oscillations with rectangular waveform observed in a modified Bonhöffer-van der Pol equation, which is considered as a circuit model for neurons of a feeding rhythm generator. In particular, we clarify a mechanism of properties in a one-parameter graph on the period of oscillations, showing a staircase with hysteresis jumps, by studying a successive bifurcation process including a chain of homoclinic bifurcations. The occurrence of homoclinic bifurcations is confirmed by using the linking number of limit cycles related with the stable manifold through an equilibrium.
ER -
English
