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On the dynamics, control and synchronization of fractional-order Ikeda map

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  • Ouannas, Adel
  • Khennaoui, Amina-Aicha
  • Odibat, Zaid
  • Pham, Viet-Thanh
  • Grassi, Giuseppe

Abstract

This paper is concerned with a fractional Caputo-difference form of Ikeda map. The dynamics of the proposed map is investigated numerically through phase plots and bifurcation diagrams considered from different perspectives. In addition, a stabilization controller is proposed and the asymptotic convergence of the states is established using the stability theory of linear fractional-order discrete systems. Furthermore, a new synchronization scheme is introduced whereby a new 2D fractional-order chaotic map is considered as the master system and the fractional-order Ikeda map is considered as the response system. Experimental investigations and numerical simulations are also provided to confirm the main findings of the study.

Suggested Citation

  • Ouannas, Adel & Khennaoui, Amina-Aicha & Odibat, Zaid & Pham, Viet-Thanh & Grassi, Giuseppe, 2019. "On the dynamics, control and synchronization of fractional-order Ikeda map," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 108-115.
    • Handle: RePEc:eee:chsofr:v:123:y:2019:i:c:p:108-115
    DOI: 10.1016/j.chaos.2019.04.002
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