Normal Form Analysis of Hopf Bifurcation Exemplified by Duffing’s Equation | Zendy

A.Y.T. Leung | Zendy; Qichang Zhang | Zendy; Yushu Chen | Zendy

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Normal Form Analysis of Hopf Bifurcation Exemplified by Duffing’s Equation

Author(s) -

A.Y.T. Leung,

Qichang Zhang,

Yushu Chen

Publication year - 1994

Publication title -

shock and vibration

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.418

H-Index - 45

eISSN - 1875-9203

pISSN - 1070-9622

DOI - 10.1155/1994/820758

Subject(s) - degenerate energy levels , hopf bifurcation , duffing equation , mathematics , pitchfork bifurcation , mathematical analysis , bifurcation , vibration , nonlinear system , saddle node bifurcation , physics , quantum mechanics

A method is proposed for calculating the normal form coefficients of the degenerate Hopf bifurcation system and the steady periodic solutions of a nonlinear vibration system. The results obtained by this method are the same as those obtained by the classical one. The present method is much simpler and can easily be implemented: that is, given the coefficients of the governing equations, the response is obtained directly by substitution.

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