A special point of Z₂-codimension three Hopf bifurcation in the Hodgkin-Huxley model

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• 作者：Hassard ; B. ; L.-J. ; Shiau
• 关键词：Hodgkin-Huxley ; Hopf bifurcation ; Singularity ; Z₂-codimension ; Degenerate Hopf bifurcation
• 刊名：Applied Mathematics Letters
• 出版年：1996
• 期刊代码：5_08939659
• 类别：mt
• 出版时间：May, 1996
• 卷：9
• 期：3
• 页码：31-34
• 文件大小：190 K

摘要

A curve in (I, T, g_Na, v_Na)-parameter space of degenerate Hopf bifurcation for the Hodgkin-Huxley model is described. The curve includes all six of the “doubly degenerate” points from our earlier work. The curve includes one special point at which m = 1, where m is the modal parameter. The recognition problem for the singularity at this point is solved. Assuming that the parameters (T, g_Na, v_Na) provide a versal unfolding, all previously known types of Hopf bifurcation behavior in the Hodgkin-Huxley system will be exhibited for (T, g_Na, v_Na) in a neighborhood of their values at this point.