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Browsing by Author "Talbi, Ibtissem"

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    Fractional Grassi-Miller Map Based on the Caputo H-Difference Operator: Linear Methods for Chaos Control and Synchronization
    (Hindawi Ltd, 2020) Ouannas, Adel; Grassi, Giuseppe; Khennaoui, Amina-Aicha; Pham, Viet-Thanh; Baleanu, Dumitru; Talbi, Ibtissem; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
    Investigating dynamic properties of discrete chaotic systems with fractional order has been receiving much attention recently. This paper provides a contribution to the topic by presenting a novel version of the fractional Grassi-Miller map, along with improved schemes for controlling and synchronizing its dynamics. By exploiting the Caputo h-difference operator, at first, the chaotic dynamics of the map are analyzed via bifurcation diagrams and phase plots. Then, a novel theorem is proved in order to stabilize the dynamics of the map at the origin by linear control laws. Additionally, two chaotic fractional Grassi-Miller maps are synchronized via linear controllers by utilizing a novel theorem based on a suitable Lyapunov function. Finally, simulation results are reported to show the effectiveness of the approach developed herein.