On fractional–order discrete–time systems: Chaos, stabilization and synchronization

Amina-Aicha Khennaoui, Adel Ouannas, Samir Bendoukha, Giuseppe Grassi, René Pierre Lozi and Viet-Thanh Pham

Chaos, Solitons & Fractals, 2019, vol. 119, issue C, 150-162

Abstract: In this paper, we propose three systems, namely the fractional Lozi map, the fractional Lorenz map, and the fractional flow map. We study some of the important dynamics of these maps including the bifurcation graphs. In addition, we propose control laws aimed at stabilizing and synchronizing a combination of these three maps. The convergence of the stabilized states and the synchronization errors is established by means of the linearization method. Numerical simulations are also presented to confirm the main findings of the study.

Keywords: Fractional discrete–time calculus; Fractional Lozi map; Fractional flow map; Fractional Lorenz map; Chaos control; Chaos synchronization (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (13)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:119:y:2019:i:c:p:150-162

DOI: 10.1016/j.chaos.2018.12.019

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