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Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.3/192057
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- Stability and multiple bifurcations of a damped harmonic oscillator with delayed feedback near zero eigenvalue singularity
- Song, Yongli; Zhang, Tonghua; Tade, Moses O.
- We investigate the dynamics of a damped harmonic oscillator with delayed feedback near zero eigenvalue singularity. We perform a linearized stability analysis and multiple bifurcations of the zero solution of the system near zero eigenvalue singularity. Taking the time delay as the bifurcation parameter, the presence of steady-state bifurcation, Bogdanov-Takens bifurcation, triple zero, and Hopf-zero singularities is demonstrated. In the case when the system has a simple zero eigenvalue, center manifold reduction and normal form theory are used to investigate the stability and the types of steady-state bifurcation. The stability of the zero solution of the system near the simple zero eigenvalue singularity is completely solved.
- Publication type
- Journal article
- Chaos, Vol. 18, no. 4 (Dec 2008), article no. 043113
- Publication year
- FOR Code(s)
- 0102 Applied Mathematics
- Bifurcation; Delays; Eigenvalues and eigenfunctions; Feedback; Harmonic oscillators; Nonlinear dynamical systems
- American Institute of Physics
- Publisher URL
- Copyright © 2008 American Institute of Physics. Published version of this paper reproduced here in accordance with the copyright policy of the publisher.
- Research Projects
Approved wavelet approaches for solving nonlinear dynamic systems in process engineering, Australian Research Council grant number DP0770420
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- Peer reviewed