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On The Study Of Delay Feedback Control And Adaptive Synchronization Near Sub-Critical Hopf Bifurcation

Author

Listed:
  • DIBAKAR GHOSH

    (Department of Mathematics, Dinabandhu Andrews College, Garia, Calcutta - 84, India;
    High Energy Physics Division, Department of Physics, Jadavpur University, Calcutta - 32, India)

  • PAPRI SAHA

    (Department of Physics, B. P. Poddar Institute of Management & Technology, Calcutta - 52, India)

  • A. ROY CHOWDHURY

    (High Energy Physics Division, Department of Physics, Jadavpur University, Calcutta - 32, India)

Abstract

The effect of delay feedback control and adaptive synchronization is studied near sub-critical Hopf bifurcation of a nonlinear dynamical system. Previously, these methods targeted the nonlinear systems near their chaotic regime but it is shown here that they are equally applicable near the branch of unstable solutions. The system is first analyzed from the view point of bifurcation, and the existence of Hopf bifurcation is established through normal form analysis. Hopf bifurcation can be either sub-critical or super-critical, and in the former case, unstable periodic orbits are formed. Our aim is to control them through a delay feedback approach so that the system stabilizes to its nearest stable periodic orbit. At the vicinity of the sub-critical Hopf point, adaptive synchronization is studied and the effect of the coupling parameter and the speed factor is analyzed in detail. Adaptive synchronization is also studied when the system is in the chaotic regime.

Suggested Citation

  • Dibakar Ghosh & Papri Saha & A. Roy Chowdhury, 2008. "On The Study Of Delay Feedback Control And Adaptive Synchronization Near Sub-Critical Hopf Bifurcation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 19(01), pages 169-185.
    • Handle: RePEc:wsi:ijmpcx:v:19:y:2008:i:01:n:s0129183108012005
    DOI: 10.1142/S0129183108012005
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