A special point of Z(2)-codimension three Hopf bifurcation in the Hodgkin-Huxley model

被引：4

作者：

Hassard, B ^{[1
]}

Shiau, LJ ^{[1
]}

机构：

[1] UNIV HOUSTON,DEPT MATH,HOUSTON,TX 77062

来源：

APPLIED MATHEMATICS LETTERS | 1996年 / 9卷 / 03期

关键词：

Hodgkin-Huxley; Hopf bifurcation; singularity; Z(2)-codimension; degenerate Hopf bifurcation;

D O I：

10.1016/0893-9659(96)00027-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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 [1,2]. 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.

引用

页码：31 / 34

页数：4