Bifurcation analysis and chaos control in Shimizu–Morioka chaotic system with delayed feedback

We investigate the local Hopf bifurcation in Shimizu–Morioka chaotic system with delayed feedback control. We choose the delay as the parameter, and the existence of local Hopf bifurcations are verified. By using the normal form theory and the center manifold theorem, we obtain the explicit formulae...

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Bibliographic Details
Published in:Applied mathematics and computation 2014-09, Vol.243, p.283-297
Main Authors: El-Dessoky, M.M., Yassen, M.T., Aly, E.S.
Format: Article
Language:English
Subjects:
Bifurcation theory
Chaos theory
Computer simulation
Control systems
Delay
Delay feedback control
Feedback control
Hopf bifurcation
Mathematical models
Numerical results
Shimizu–Morioka system
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Summary:We investigate the local Hopf bifurcation in Shimizu–Morioka chaotic system with delayed feedback control. We choose the delay as the parameter, and the existence of local Hopf bifurcations are verified. By using the normal form theory and the center manifold theorem, we obtain the explicit formulae for determining the stability and direction of bifurcated periodic solutions. Numerical simulations indicate that delayed feedback control plays an effective role in control of chaos.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2014.05.072