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

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

Chaos, Solitons & Fractals, 2019, vol. 123, issue C, 108-115

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.

Keywords: Fractional discrete–time calculus; Caputo-like difference operator; Chaos; Ikeda map; Control; Synchronization (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (9)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:123:y:2019:i:c:p:108-115

DOI: 10.1016/j.chaos.2019.04.002

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