Ouannas, AdelGrassi, GiuseppeKhennaoui, Amina-AichaPham, Viet-ThanhBaleanu, DumitruTalbi, Ibtissem2022-04-292025-09-182022-04-292025-09-182020Talbi, Ibtissem...et al. (2020). "Fractional Grassi–Miller map based on the Caputo H-difference operator: Linear methods for chaos control and synchronization", Discrete Dynamics in Nature and Society, Vol. 2020.1026-02261607-887Xhttps://doi.org/10.1155/2020/8825694https://hdl.handle.net/20.500.12416/12026Khennaoui, Amina Aicha/0000-0002-7109-197X; Ouannas, Adel/0000-0001-9611-2047Investigating 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.eninfo:eu-repo/semantics/openAccessArticle10.1155/2020/88256942-s2.0-85106549208