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Volumn 82, Issue 3, 2000, Pages 223-229

Hopf bifurcations in multiple-parameter space of the Hodgkin-Huxley equations II. Singularity theoretic approach and highly degenerate bifurcations

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; BIOLOGICAL MODEL; CELL MEMBRANE POTENTIAL; MATHEMATICAL COMPUTING; MATHEMATICS; NERVE FIBER; PERIODICITY; PHYSIOLOGY;

EID: 0034145131     PISSN: 03401200     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004220050022     Document Type: Article
Times cited : (26)

References (14)
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    • (1986) Applied Mathematics Report
    • Doedel, E.1    Kernevez, J.P.2
  • 2
    • 0034145622 scopus 로고    scopus 로고
    • Hopf bifurcations in multiple parameter space of the Hodgkin-Huxley equations. I. Global organization of bistable periodic solutions
    • Fukai H, Doi S, Nomura T, Sato S (1999) Hopf bifurcations in multiple parameter space of the Hodgkin-Huxley equations. I. Global organization of bistable periodic solutions. Biol Cybern 82:215-222
    • (1999) Biol Cybern , vol.82 , pp. 215-222
    • Fukai, H.1    Doi, S.2    Nomura, T.3    Sato, S.4
  • 5
    • 0017854654 scopus 로고
    • Bifurcation of periodic solutions of the Hodgkin-Huxley model for the squid giant axon
    • Hassard B (1978) Bifurcation of periodic solutions of the Hodgkin-Huxley model for the squid giant axon. J Theor Biol 71:401-420
    • (1978) J Theor Biol , vol.71 , pp. 401-420
    • Hassard, B.1
  • 6
    • 0024601417 scopus 로고
    • Isolated periodic solutions of the Hodgkin-Huxley equations
    • Hassard BD, Shiau LJ (1989) Isolated periodic solutions of the Hodgkin-Huxley equations. J Theor Biol 136:267-280
    • (1989) J Theor Biol , vol.136 , pp. 267-280
    • Hassard, B.D.1    Shiau, L.J.2
  • 7
    • 0040663700 scopus 로고    scopus 로고
    • 2-codimension three Hopf bifurcation in the Hodgkin-Huxley model
    • 2-codimension three Hopf bifurcation in the Hodgkin-Huxley model. Appl Math Lett 9:31-34
    • (1996) Appl Math Lett , vol.9 , pp. 31-34
    • Hassard, B.D.1    Shiau, L.J.2
  • 8
    • 35649001607 scopus 로고
    • A quantitative description of membrane current and its application to conduction and excitation in nerve
    • Lond
    • Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol (Lond) 117:504-544
    • (1952) J Physiol , vol.117 , pp. 504-544
    • Hodgkin, A.L.1    Huxley, A.F.2
  • 9
    • 0039478436 scopus 로고
    • Degenerate Hopf bifurcation and nerve impulse
    • Labouriau IS (1985) Degenerate Hopf bifurcation and nerve impulse. SIAM J Math Anal 16:1121-1133
    • (1985) SIAM J Math Anal , vol.16 , pp. 1121-1133
    • Labouriau, I.S.1
  • 10
    • 0037580095 scopus 로고
    • Degenerate Hopf bifurcation and nerve impulse. Part II
    • Labouriau IS (1989) Degenerate Hopf bifurcation and nerve impulse. Part II. SIAM J Math Anal 20:1-12
    • (1989) SIAM J Math Anal , vol.20 , pp. 1-12
    • Labouriau, I.S.1
  • 11
    • 0018234671 scopus 로고
    • On repetitive activity in nerve
    • Rinzel J (1978) On repetitive activity in nerve. Fed Proc 37:2793-2802
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    • Rinzel, J.1
  • 12
    • 0019310660 scopus 로고
    • Numerical calculation of stable and unstable periodic solutions to the Hodgkin-Huxley equations
    • Rinzel J, Miller RN (1980) Numerical calculation of stable and unstable periodic solutions to the Hodgkin-Huxley equations. Math Biosci 49:27-59
    • (1980) Math Biosci , vol.49 , pp. 27-59
    • Rinzel, J.1    Miller, R.N.2
  • 13
    • 0026020931 scopus 로고
    • Degenerate Hopf bifurcation and isolated periodic solutions of the Hodgkin-Huxley model with varying sodium ion concentration
    • Shiau LJ, Hassard B (1991) Degenerate Hopf bifurcation and isolated periodic solutions of the Hodgkin-Huxley model with varying sodium ion concentration. J Theor Biol 148:157-173
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    • Shiau, L.J.1    Hassard, B.2
  • 14
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    • The bifurcation of periodic solutions in the Hodgkin-Huxley equations
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* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.