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

Article type: Research Article

Authors: Leung, A.Y.T. | Qichang, Zhang | Yushu, Chen

Affiliations: Department of Civil and Structural Engineering, University of Hong Kong, Hong Kong | Department of Mechanics, Tianjin University, China

Abstract: 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.

DOI: 10.3233/SAV-1994-1303

Journal: Shock and Vibration, vol. 1, no. 3, pp. 233-240, 1994