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Numerical Computation of Degenerate Hopf Bifurcation Points
Author(s) -
Xu Haihong,
Werner Bodo,
Janovský Vladimír
Publication year - 1998
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/(sici)1521-4001(199812)78:12<807::aid-zamm807>3.0.co;2-c
Subject(s) - mathematics , hopf bifurcation , degenerate energy levels , computation , mathematical analysis , bifurcation , numerical analysis , bifurcation theory , numerical stability , saddle node bifurcation , equivalence (formal languages) , nonlinear system , pure mathematics , physics , algorithm , quantum mechanics
In this paper a numerical method for the detection and computation of degenerate Hopf bifurcation points is presented. The degeneracies are classified and defining equations characterizing each of the equivalence classes are constructed by means of a generalized Liapunov‐Schmidt reduction. The numerical computation of the sign of the first Liapunov coefficient which determines the stability of the bifurcating periodic orbits is discussed as well. Numerical experiments are performed for the clamped Hodgkin‐Huxley equations.