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Chaos control of integer and fractional orders of chaotic Burke–Shaw system using time delayed feedback control

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  • Mahmoud, Gamal M.
  • Arafa, Ayman A.
  • Abed-Elhameed, Tarek M.
  • Mahmoud, Emad E.

Abstract

The aim of this paper is to investigate the control of chaotic Burke-Shaw system using Pyragas method. This system is derived from Lorenz system which has several applications in physics and engineering (e.g. secure communications). The linear stability and the existence of Hopf bifurcation of this system are investigated. Based on the characteristic equation, a theorem is stated and proved. This theorem is used to calculate the interval values of the time delay τ at which this system is stable (unstable). By establishing appropriate time delay τ and feedback strength K ranges, one of the unstable equilibria of this system can be controlled to be stable.

Suggested Citation

  • Mahmoud, Gamal M. & Arafa, Ayman A. & Abed-Elhameed, Tarek M. & Mahmoud, Emad E., 2017. "Chaos control of integer and fractional orders of chaotic Burke–Shaw system using time delayed feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 680-692.
    • Handle: RePEc:eee:chsofr:v:104:y:2017:i:c:p:680-692
    DOI: 10.1016/j.chaos.2017.09.023
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