Two-parameter bifurcations in the Hodgkin-Huxley equations for muscle fibers
作者： Kazuko Terada , Hisa-Aki Tanaka , Shuji Yoshizawa
DOI: 10.1002/(SICI)1520-6440(200006)83:6<86::AID-ECJC10>3.0.CO;2-C
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摘要: In order to reveal the mechanism behind ion channel diseases of muscles, we numerically analyzed bifurcations in space-clamped Hodgkin–Huxley equations for muscles frogs (HHM). The leakage conductance gl and sodium effective bias voltage V m were selected as bifurcation parameters. We continued codimension-one branches saddle node, homoclinic, Hopf, double cycle on × g l plane. showed existence codimension-two points: a twisted resonant, Bogdanov–Takens, an inclination-flip (if), degenerate cusp. first three found HHM with parameters within realistic range. if point is be key behavior HHM, around which parameter plane separated into regions: normal action potential, repetitive firing (myotonia), depolarized resting potential (periodic paralysis). characteristics are not yet completely revealed theoretically, so our results also mathematical interest. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 83(6): 86–94,
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