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On the Analysis of Hopf Bifurcation associated with a Two-Fold Zero Eigenvalue, part 2: Non-autonomous System

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Tue, 2015-11-17 15:46 — Munther Diyab Hussein Ibrahim
Journal Title, Volume, Page: 
Journal of Vibration and Acoustics (American Association of Mechanical Engineering
Year of Publication: 
1999
Link: 
http://vibrationacoustics.asmedigitalcollection.asme.org/article.aspx?articleid=...
Authors: 
M. MOH’D,
an-najah university
Current Affiliation: 
an-najah university
[email protected]
K. HUSEYIN.
Preferred Abstract (Original): 
The static and dynamic bifurcations of an autonomous system associated with a twofold zero eigenvalue (of index one) are studied. Attention is focused on Hopf bifurcation solutions in the neighborhood of such a singularity. The family of limit cycles are analyzed fully by applying the formula type results of the Intrinsic Harmonic Balancing method. Thus, parameter-amplitude and amplitude-frequency relationships as well as an ordered form of approximations for the periodic motions are obtained explicitly. A verification technique, with the aid of MAPLE, is used to show the consistency of ordered approximations.