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

• Published in: Chaos, solitons and fractals Vol. 123; pp. 108 - 115
• Main Authors: Ouannas, Adel, Khennaoui, Amina-Aicha, Odibat, Zaid, Pham, Viet-Thanh, Grassi, Giuseppe
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.06.2019
• Subjects: Caputo-like difference operator; Chaos; Control; Fractional discrete–time calculus; Ikeda map; Synchronization; Chaos; Control; Fractional discrete–time calculus; Caputo-like difference operator; Synchronization; Ikeda map
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2019.04.002

•A fractional Caputo-difference form of Ikeda map is presented.•Chaotic dynamics of fractional Ikeda map is studied.•Control schemes to stabilize and synchronize fractional Ikeda map are discussed. 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.