### Abstract

Bifurcation characteristics in the modified Hodgkin-Huxley equations are investigated in detail on the basis of a recently presented theory, which can describe normally bifurcating as well as invertedly-bifurcating hard-mode instabilities. An algebraic-processing computer language was used to get analytic expressions in perturbative calculations up to the fifth order. The present theoretical results can describe the full bifurcation diagram for the case where normally and invertedly bifurcation diagram for the case where normally and invertedly bifurcating instability points coexist closely. It is also shown that the present theory can describe even an interesting example of the bifurcation diagram which is formed by a single continuous closed branch composed of unstable and stable self-oscillations without any instability point.

Original language | English |
---|---|

Pages (from-to) | 9-53 |

Number of pages | 45 |

Journal | Memoirs of the Kyushu University, Faculty of Engineering |

Volume | 43 |

Issue number | 1 |

Publication status | Published - Jan 1 1983 |

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### All Science Journal Classification (ASJC) codes

- Energy(all)
- Atmospheric Science
- Earth and Planetary Sciences(all)
- Management of Technology and Innovation

### Cite this

*Memoirs of the Kyushu University, Faculty of Engineering*,

*43*(1), 9-53.

**INVERTEDLY-BIFURCATING SELF-OSCILLATIONS IN THE MODIFIED HODGKIN-HUXLEY EQUATIONS.** / Ryu, Kouichi; Ezaki, Shu; Toko, Kiyoshi.

Research output: Contribution to journal › Article

*Memoirs of the Kyushu University, Faculty of Engineering*, vol. 43, no. 1, pp. 9-53.

}

TY - JOUR

T1 - INVERTEDLY-BIFURCATING SELF-OSCILLATIONS IN THE MODIFIED HODGKIN-HUXLEY EQUATIONS.

AU - Ryu, Kouichi

AU - Ezaki, Shu

AU - Toko, Kiyoshi

PY - 1983/1/1

Y1 - 1983/1/1

N2 - Bifurcation characteristics in the modified Hodgkin-Huxley equations are investigated in detail on the basis of a recently presented theory, which can describe normally bifurcating as well as invertedly-bifurcating hard-mode instabilities. An algebraic-processing computer language was used to get analytic expressions in perturbative calculations up to the fifth order. The present theoretical results can describe the full bifurcation diagram for the case where normally and invertedly bifurcation diagram for the case where normally and invertedly bifurcating instability points coexist closely. It is also shown that the present theory can describe even an interesting example of the bifurcation diagram which is formed by a single continuous closed branch composed of unstable and stable self-oscillations without any instability point.

AB - Bifurcation characteristics in the modified Hodgkin-Huxley equations are investigated in detail on the basis of a recently presented theory, which can describe normally bifurcating as well as invertedly-bifurcating hard-mode instabilities. An algebraic-processing computer language was used to get analytic expressions in perturbative calculations up to the fifth order. The present theoretical results can describe the full bifurcation diagram for the case where normally and invertedly bifurcation diagram for the case where normally and invertedly bifurcating instability points coexist closely. It is also shown that the present theory can describe even an interesting example of the bifurcation diagram which is formed by a single continuous closed branch composed of unstable and stable self-oscillations without any instability point.

UR - http://www.scopus.com/inward/record.url?scp=0020720086&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0020720086&partnerID=8YFLogxK

M3 - Article

VL - 43

SP - 9

EP - 53

JO - Memoirs of the Faculty of Engineering, Kyushu University

JF - Memoirs of the Faculty of Engineering, Kyushu University

SN - 1345-868X

IS - 1

ER -