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".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
우리는 먹이 리듬 생성기의 뉴런에 대한 회로 모델로 간주되는 수정된 Bonhöffer-van der Pol 방정식에서 관찰된 직사각형 파형을 사용하여 버스트 진동의 분기를 조사합니다. 특히, 우리는 동종사상 분기점 체인을 포함하는 연속적인 분기 과정을 연구함으로써 히스테리시스 점프가 있는 계단을 보여주는 진동 주기에 대한 1-매개변수 그래프의 특성 메커니즘을 명확히 합니다. 평형을 통한 안정 다양체와 관련된 한계주기의 연결수를 이용하여 동종사상 분기의 발생을 확인합니다.
수정된 BVP 방정식, 분기, 동형궤도, 혼돈, 신경 모델
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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},}
부
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 -