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Volumn 83, Issue 6, 2000, Pages 86-94

Two-parameter bifurcations in the Hodgkin-Huxley equations for muscle fibers

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); BIOLOGICAL MEMBRANES; DISEASES; MUSCLE; NUMERICAL ANALYSIS;

EID: 0033870936     PISSN: 10420967     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1520-6440(200006)83:6<86::AID-ECJC10>3.0.CO;2-C     Document Type: Article
Times cited : (9)

References (32)
  • 1
    • 0030668811 scopus 로고    scopus 로고
    • Ion channel mutations and diseases of skeletal muscle
    • Barchi RL. Ion channel mutations and diseases of skeletal muscle. Neurobio Dis 1997;4:254-264.
    • (1997) Neurobio Dis , vol.4 , pp. 254-264
    • Barchi, R.L.1
  • 3
    • 24544472610 scopus 로고    scopus 로고
    • Bifurcations of periodic solutions of the Hodgkin-Huxley equations for muscle fibers
    • in Japanese
    • Kazuko T, Shuji Y. Chiaki N. Bifurcations of periodic solutions of the Hodgkin-Huxley equations for muscle fibers. Trans IEICE 1997;J80-A:I960-1967. (in Japanese)
    • (1997) Trans IEICE , vol.J80-A
    • Kazuko, T.1    Shuji, Y.2    Chiaki, N.3
  • 4
    • 35649001607 scopus 로고
    • A quantitative description of membrane current and its applications to conduction and excitation in nerve
    • Hodgkin AL, Huxley AF. A quantitative description of membrane current and its applications to conduction and excitation in nerve. J Physiol London 1952;117:500-544.
    • (1952) J Physiol London , vol.117 , pp. 500-544
    • Hodgkin, A.L.1    Huxley, A.F.2
  • 5
    • 0023238072 scopus 로고
    • Muscle chloride channels
    • Bretag AH. Muscle chloride channels. Physiol Rev 1987;67:618-724.
    • (1987) Physiol Rev , vol.67 , pp. 618-724
    • Bretag, A.H.1
  • 6
    • 0021811103 scopus 로고
    • Membrane changes in cells from myotonia patients
    • Rüdel R, Lehmann-Horn F. Membrane changes in cells from myotonia patients. Physiol Rev 1985;65:310-356.
    • (1985) Physiol Rev , vol.65 , pp. 310-356
    • Rüdel, R.1    Lehmann-Horn, F.2
  • 7
    • 0030068496 scopus 로고    scopus 로고
    • Ion-channel defects and aberrant excitability in myotonia and periodic paralysis
    • Cannon SC. Ion-channel defects and aberrant excitability in myotonia and periodic paralysis. Trends Neurosci 1996;19:3-10.
    • (1996) Trends Neurosci , vol.19 , pp. 3-10
    • Cannon, S.C.1
  • 9
    • 0342642762 scopus 로고
    • An introduction to numerical analysis: Focus on ordinary differential equations
    • in Japanese
    • Taketomo M. An introduction to numerical analysis: Focus on ordinary differential equations. Asakurashoten; 1985. p 82-86. (in Japanese)
    • (1985) Asakurashoten , pp. 82-86
    • Taketomo, M.1
  • 11
    • 0001811061 scopus 로고
    • ODEPACK: A systemized collection of ODE solvers
    • Stepleman RS et al., editors. North-Holland
    • Hindmarsh AC. ODEPACK: A systemized collection of ODE solvers. In: Stepleman RS et al., editors. Scientific computing. North-Holland; 1983. p 55-64.
    • (1983) Scientific Computing , pp. 55-64
    • Hindmarsh, A.C.1
  • 12
    • 0000536084 scopus 로고
    • Automatic selection of methods for solving stiff and nonstiff systems of ordinary differential equations
    • Petzold LR. Automatic selection of methods for solving stiff and nonstiff systems of ordinary differential equations. SIAM J Sci Statist Comput 1983;4:136-148.
    • (1983) SIAM J Sci Statist Comput , vol.4 , pp. 136-148
    • Petzold, L.R.1
  • 13
    • 6344238035 scopus 로고
    • An active pulse transmission line simulating nerve axon
    • Nagumo J, Arimoto S, Yoshizawa S. An active pulse transmission line simulating nerve axon. Proc IRE 1962;50:2061-2070.
    • (1962) Proc IRE , vol.50 , pp. 2061-2070
    • Nagumo, J.1    Arimoto, S.2    Yoshizawa, S.3
  • 14
    • 0343948793 scopus 로고
    • Periodic firing in muscle membrane at low chloride conductance
    • Terada K, Yoshizawa S, Nishimura C. Periodic firing in muscle membrane at low chloride conductance. Trans IEICE 1991;E74:999-1002.
    • (1991) Trans IEICE , vol.E74 , pp. 999-1002
    • Terada, K.1    Yoshizawa, S.2    Nishimura, C.3
  • 15
    • 0001215210 scopus 로고
    • On the generation of a periodic motion from trajectories doubly asymptotic to an equilibrium state of saddle type
    • Shil'nikov LP. On the generation of a periodic motion from trajectories doubly asymptotic to an equilibrium state of saddle type. Math USSR Sborn 1968;6:427-438.
    • (1968) Math USSR Sborn , vol.6 , pp. 427-438
    • Shil'nikov, L.P.1
  • 16
    • 0343076896 scopus 로고
    • Bifurcations of orbits homoclinic and heteroclinic to hyperbolic equilibria
    • Elements of applied bifurcation theory Springer-Verlag
    • Kuznetsov YA. Bifurcations of orbits homoclinic and heteroclinic to hyperbolic equilibria. In: Elements of applied bifurcation theory (Applied Mathematical Sciences Vol. 112). Springer-Verlag; 1995. p 178-213.
    • (1995) Applied Mathematical Sciences , vol.112 , pp. 178-213
    • Kuznetsov, Y.A.1
  • 17
    • 0024601417 scopus 로고
    • Isolated periodic solutions of the Hodgkin-Huxley equations
    • Hassard BD, Shiau LJ. Isolated periodic solutions of the Hodgkin-Huxley equations. J Theor Biol 1989;136:267-280.
    • (1989) J Theor Biol , vol.136 , pp. 267-280
    • Hassard, B.D.1    Shiau, L.J.2
  • 18
    • 0026020931 scopus 로고
    • Degenerate Hopf bifurcation and isolated periodic solutions of the Hodgkin-Huxley model with varying sodium ion concentration
    • Shiau LJ, Hassard BD. Degenerate Hopf bifurcation and isolated periodic solutions of the Hodgkin-Huxley model with varying sodium ion concentration. J Theor Biol 1991;148:157-173.
    • (1991) J Theor Biol , vol.148 , pp. 157-173
    • Shiau, L.J.1    Hassard, B.D.2
  • 20
    • 0000370809 scopus 로고
    • Bifurcation of the Hodgkin and Huxley equations: A new twist
    • Guckenheimer J, Labouriau IS. Bifurcation of the Hodgkin and Huxley equations: A new twist. Bull Math Biol 1993;55:937-952.
    • (1993) Bull Math Biol , vol.55 , pp. 937-952
    • Guckenheimer, J.1    Labouriau, I.S.2
  • 21
    • 0028548427 scopus 로고
    • On computing connecting orbits: General algorithm and applications to the Sine-Gordon and Hodgkin-Huxley equations
    • Doedel EJ, Friedman MJ, Guckenheimer J. On computing connecting orbits: General algorithm and applications to the Sine-Gordon and Hodgkin-Huxley equations. IEICE Trans Fundam 1994;E77-A:1801-1804.
    • (1994) IEICE Trans Fundam , vol.E77-A , pp. 1801-1804
    • Doedel, E.J.1    Friedman, M.J.2    Guckenheimer, J.3
  • 22
    • 0039478436 scopus 로고
    • Degenerate Hopf bifurcation and nerve impulse
    • Labouriau IS. Degenerate Hopf bifurcation and nerve impulse. SIAM J Math Anal 1985;16:1121-1133.
    • (1985) SIAM J Math Anal , vol.16 , pp. 1121-1133
    • Labouriau, I.S.1
  • 23
    • 0037580095 scopus 로고
    • Degenerate Hopf bifurcation and nerve impulse: Part II
    • Labouriau IS. Degenerate Hopf bifurcation and nerve impulse: Part II. SIAM J Math Anal 1989;20:1-12.
    • (1989) SIAM J Math Anal , vol.20 , pp. 1-12
    • Labouriau, I.S.1
  • 24
    • 0000184573 scopus 로고
    • Homoclinic bifurcation at resonant eigenvalues
    • Chow SN, Deng B, Fiedler B. Homoclinic bifurcation at resonant eigenvalues. J Dyn Diff Eq 1990;2:177-244.
    • (1990) J Dyn Diff Eq , vol.2 , pp. 177-244
    • Chow, S.N.1    Deng, B.2    Fiedler, B.3
  • 25
    • 0001002402 scopus 로고
    • Bifurcations to N-homoclinic orbits and N-periodic orbits in vector fields
    • Kisaka M, Kokubu H, Oka H. Bifurcations to N-homoclinic orbits and N-periodic orbits in vector fields. J Dynam Diff Eq 1993;5:305-357.
    • (1993) J Dynam Diff Eq , vol.5 , pp. 305-357
    • Kisaka, M.1    Kokubu, H.2    Oka, H.3
  • 26
    • 0000933820 scopus 로고    scopus 로고
    • N-Homoclinic bifurcations for homoclinic orbits changing their twisting
    • Nii S. N-Homoclinic bifurcations for homoclinic orbits changing their twisting. J Dyn Diff Eq 1996;8:549-572.
    • (1996) J Dyn Diff Eq , vol.8 , pp. 549-572
    • Nii, S.1
  • 27
    • 0001559874 scopus 로고
    • The cusp horse-shoe and its bifurcations from inclination-flip homoclinic orbits
    • Homburg AJ, Kokubu H, Krupa M. The cusp horse-shoe and its bifurcations from inclination-flip homoclinic orbits. Ergod Theory Dyn Syst 1994;14:667-693.
    • (1994) Ergod Theory Dyn Syst , vol.14 , pp. 667-693
    • Homburg, A.J.1    Kokubu, H.2    Krupa, M.3
  • 30
    • 21844486228 scopus 로고
    • Numerical detection and continuation of codimension-two homoclinic bifurcations
    • Champneys AR, Kuznetsov YA. Numerical detection and continuation of codimension-two homoclinic bifurcations. Int J Bifurcation Chaos 1994;4:785-822.
    • (1994) Int J Bifurcation Chaos , vol.4 , pp. 785-822
    • Champneys, A.R.1    Kuznetsov, Y.A.2
  • 31
    • 0342642754 scopus 로고    scopus 로고
    • Numerical verification of existence of solutions
    • Science Inc.; in Japanese
    • Shinichi O. Numerical verification of existence of solutions. Surikagaku No. 394, p 69-77. Science Inc.; 1996. (in Japanese)
    • (1996) Surikagaku , vol.394 , pp. 69-77
    • Shinichi, O.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.