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Browsing by Author "Viet-Thanh Pham"

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    Article
    Citation - WoS: 5
    Citation - Scopus: 11
    Bifurcations, Hidden Chaos and Control in Fractional Maps
    (Mdpi, 2020) Ouannas, Adel; Almatroud, Othman Abdullah; Khennaoui, Amina Aicha; Alsawalha, Mohammad Mossa; Baleanu, Dumitru; Van Van Huynh; Viet-Thanh Pham; 56389; Matematik
    Recently, hidden attractors with stable equilibria have received considerable attention in chaos theory and nonlinear dynamical systems. Based on discrete fractional calculus, this paper proposes a simple two-dimensional and three-dimensional fractional maps. Both fractional maps are chaotic and have a unique equilibrium point. Results show that the dynamics of the proposed fractional maps are sensitive to both initial conditions and fractional order. There are coexisting attractors which have been displayed in terms of bifurcation diagrams, phase portraits and a 0-1 test. Furthermore, control schemes are introduced to stabilize the chaotic trajectories of the two novel systems.
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    Article
    Citation - WoS: 3
    Citation - Scopus: 4
    HYPERCHAOTIC DYNAMICS of A NEW FRACTIONAL DISCRETE-TIME SYSTEM
    (World Scientific Publ Co Pte Ltd, 2021) Khennaoui, Amina-Aicha; Ouannas, Adel; Momani, Shaher; Dibi, Zohir; Grassi, Giuseppe; Baleanu, Dumitru; Viet-Thanh Pham; 56389; Matematik
    In recent years, some efforts have been devoted to nonlinear dynamics of fractional discrete-time systems. A number of papers have so far discussed results related to the presence of chaos in fractional maps. However, less results have been published to date regarding the presence of hyperchaos in fractional discrete-time systems. This paper aims to bridge the gap by introducing a new three-dimensional fractional map that shows, for the first time, complex hyperchaotic behaviors. A detailed analysis of the map dynamics is conducted via computation of Lyapunov exponents, bifurcation diagrams, phase portraits, approximated entropy and C-0 complexity. Simulation results confirm the effectiveness of the approach illustrated herein.