Hodgkin-Huxley 方程式の周期解の大域的分岐構造  [in Japanese] Global Bifurcation Structure of Periodic Solutions in Hodgkin-Huxley Equations  [in Japanese]

Access this Article

Search this Article

Author(s)

    • 深井 英和 FUKAI Hidekazu
    • 大阪大学基礎工学部生物工学科 Department of Biophysical Engineering, Faculty of Engineering Science, Osaka University
    • 野村 泰伸 NOMURA Taishin
    • 大阪大学基礎工学部生物工学科 Department of Biophysical Engineering, Faculty of Engineering Science, Osaka University
    • PAKDAMAN Khashayar
    • 大阪大学基礎工学部生物工学科 Department of Biophysical Engineering, Faculty of Engineering Science, Osaka University
    • 土居 伸二 DOI Shinji
    • 大阪大学基礎工学部生物工学科 Department of Biophysical Engineering, Faculty of Engineering Science, Osaka University
    • 佐藤 俊輔 SATO Shunsuke
    • 大阪大学基礎工学部生物工学科 Department of Biophysical Engineering, Faculty of Engineering Science, Osaka University

Abstract

The Hodgkin-Huxley equations (Hodgkin & Huxley 1952) are a neuron model describing electrical excitation of the squid giant axon membrane. By examining the global bifurcation structure of these equations, we found a degenerate Hopf bifurcation point. Several stable periodic orbits coexist in the neighborhood of this point. We determined parameter ranges where such multistability occurs and delimited regions where either two stable periodic solutions, or two stable periodic solutions and a stable equilibrium point coexist. We argue that comparison between the global bifurcation structure experimental data provides insight into the domain of validity of the Hodgkin-Huxley equations.

Journal

  • The Brain & Neural Networks

    The Brain & Neural Networks 4(2), 83-91, 1997-06-05

    Japanese Neural Network Society

References:  19

Cited by:  5

Codes

  • NII Article ID (NAID)
    10008841328
  • NII NACSIS-CAT ID (NCID)
    AA11658570
  • Text Lang
    JPN
  • Article Type
    Journal Article
  • ISSN
    1340766X
  • Data Source
    CJP  CJPref  J-STAGE 
Page Top