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Chaos : Stability and multiple bifurcations of a damped harmonic oscillator with delayed feedback near zero eigenvalue singularity

By Yongli Song, Tonghua Zhang, and Moses O. Tadé

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Book Id: WPLBN0002169295
Format Type: PDF eBook :
File Size: Serial Publication
Reproduction Date: 14 November 2008

Title: Chaos : Stability and multiple bifurcations of a damped harmonic oscillator with delayed feedback near zero eigenvalue singularity  
Author: Yongli Song, Tonghua Zhang, and Moses O. Tadé
Volume: Issue : November 2008
Language: English
Subject: Science, Physics, Natural Science
Collections: Periodicals: Journal and Magazine Collection (Contemporary), Chaos Collection
Historic
Publication Date:
Publisher: American Institute of Physics

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Tonghua Zhang, And Moses O. Tad, Y. S. (n.d.). Chaos : Stability and multiple bifurcations of a damped harmonic oscillator with delayed feedback near zero eigenvalue singularity. Retrieved from http://worldebookfair.com/


Description
Description: 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.

 

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