Hopf Bifurcation Analysis and Chaos Control of a Chaotic System without rho ilnikov Orbits

This paper mainly investigates the dynamical behaviors of a chaotic system without DELETE ilnikov orbits by the normal form theory. Both the stability of the equilibria and the existence of local Hopf bifurcation are proved in view of analyzing the associated characteristic equation. Meanwhile, the...

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Bibliographic Details
Published in:Discrete dynamics in nature and society 2015-01, Vol.2015
Main Authors: Li, Na, Tan, Wei, Zhao, Huitao
Format: Article
Language:English
Subjects:
Chaos theory
Delay
Dynamical systems
Dynamics
Hopf bifurcation
Mathematical analysis
Mathematical models
Orbits
Online Access:Get full text
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Summary:This paper mainly investigates the dynamical behaviors of a chaotic system without DELETE ilnikov orbits by the normal form theory. Both the stability of the equilibria and the existence of local Hopf bifurcation are proved in view of analyzing the associated characteristic equation. Meanwhile, the direction and the period of bifurcating periodic solutions are determined. Regarding the delay as a parameter, we discuss the effect of time delay on the dynamics of chaotic system with delayed feedback control. Finally, numerical simulations indicate that chaotic oscillation is converted into a steady state when the delay passes through a certain critical value.
ISSN:1026-0226
1607-887X
DOI:10.1155/2015/912798