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Hopf bifurcation and chaos in fractional-order modified hybrid optical system

Hopf bifurcation and chaos in fractional-order modified hybrid optical system In this paper, a chaotic fractional-order modified hybrid optical system is presented. Some basic dynamical properties are further investigated by means of Poincaré mapping, parameter phase portraits, and the largest Lyapunov exponents. Fractional Hopf bifurcation conditions are proposed; it is found that Hopf bifurcation occurs on the proposed system when the fractional-order varies and passes a sequence of critical values. The chaotic motion is validated by the positive Lyapunov exponent. Finally, some numerical simulations are also carried out to illustrate our results. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Dynamics Springer Journals

Hopf bifurcation and chaos in fractional-order modified hybrid optical system

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References (29)

Publisher
Springer Journals
Copyright
Copyright © 2011 by Springer Science+Business Media B.V.
Subject
Engineering; Automotive Engineering; Mechanics; Mechanical Engineering; Vibration, Dynamical Systems, Control
ISSN
0924-090X
eISSN
1573-269X
DOI
10.1007/s11071-011-0263-4
Publisher site
See Article on Publisher Site

Abstract

In this paper, a chaotic fractional-order modified hybrid optical system is presented. Some basic dynamical properties are further investigated by means of Poincaré mapping, parameter phase portraits, and the largest Lyapunov exponents. Fractional Hopf bifurcation conditions are proposed; it is found that Hopf bifurcation occurs on the proposed system when the fractional-order varies and passes a sequence of critical values. The chaotic motion is validated by the positive Lyapunov exponent. Finally, some numerical simulations are also carried out to illustrate our results.

Journal

Nonlinear DynamicsSpringer Journals

Published: Nov 23, 2011

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