The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Nous étudions les bifurcations d'oscillations en rafale avec une forme d'onde rectangulaire observées dans une équation de Bonhöffer-van der Pol modifiée, considérée comme un modèle de circuit pour les neurones d'un générateur de rythme d'alimentation. En particulier, nous clarifions un mécanisme de propriétés dans un graphe à un paramètre sur la période des oscillations, montrant un escalier avec des sauts d'hystérésis, en étudiant un processus de bifurcation successive incluant une chaîne de bifurcations homocliniques. L'apparition de bifurcations homocliniques est confirmée en utilisant le nombre de cycles limites liés à la variété stable via un équilibre.
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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 -