Browsing by Author "Pham, Viet-Thanh"

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Citation Count: Ouannas, Adel...et al. (2020). "Bifurcations, Hidden Chaos and Control in Fractional Maps", Symmetry-Basel, Vol. 12, No. 6.
Bifurcations, Hidden Chaos and Control in Fractional Maps
(2020) Ouannas, Adel; Almatroud, Othman Abdullah; Khennaoui, Amina Aicha; Alsawalha, Mohammad Mossa; Baleanu, Dumitru; Huynh, Van Van; Pham, Viet-Thanh; 56389
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.
Citation Count: Ahmad, Israr...et al. (2021). "Finite-time stabilization of a perturbed chaotic finance model", Journal of Advanced Research, vol. 32, pp. 1-14.
Finite-time stabilization of a perturbed chaotic finance model
(2021) Ahmad, Israr; Ouannas, Adel; Shafiq, Muhammad; Pham, Viet-Thanh; Baleanu, Dumitru; 56389
Introduction: Robust, stable financial systems significantly improve the growth of an economic system. The stabilization of financial systems poses the following challenges. The state variables’ trajectories (i) lie outside the basin of attraction, (ii) have high oscillations, and (iii) converge to the equilibrium state slowly. Objectives: This paper aims to design a controller that develops a robust, stable financial closed-loop system to address the challenges above by (i) attracting all state variables to the origin, (ii) reducing the oscillations, and (iii) increasing the gradient of the convergence. Methods: This paper proposes a detailed mathematical analysis of the steady-state stability, dissipative characteristics, the Lyapunov exponents, bifurcation phenomena, and Poincare maps of chaotic financial dynamic systems. The proposed controller does not cancel the nonlinear terms appearing in the closed-loop. This structure is robust to the smoothly varying system parameters and improves closed-loop efficiency. Further, the controller eradicates the effects of inevitable exogenous disturbances and accomplishes a faster, oscillation-free convergence of the perturbed state variables to the desired steady-state within a finite time. The Lyapunov stability analysis proves the closed-loop global stability. The paper also discusses finite-time stability analysis and describes the controller parameters’ effects on the convergence rates. Computer-based simulations endorse the theoretical findings, and the comparative study highlights the benefits. Results: Theoretical analysis proofs and computer simulation results verify that the proposed controller compels the state trajectories, including trajectories outside the basin of attraction, to the origin within finite time without oscillations while being faster than the other controllers discussed in the comparative study section. Conclusions: This article proposes a novel robust, nonlinear finite-time controller for the robust stabilization of the chaotic finance model. It provides an in-depth analysis based on the Lyapunov stability theory and computer simulation results to verify the robust convergence of the state variables to the origin. © 2021
Citation Count: Talbi, 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.
Fractional Grassi–Miller map based on the Caputo H-difference operator: Linear methods for chaos control and synchronization
(2020) Talbi, Ibtissem; Ouannas, Adel; Grassi, Giuseppe; Khennaoui, Amina-Aicha; Pham, Viet-Thanh; Baleanu, Dumitru; 56389
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. Copyright © 2020 Ibtissem Talbi et al.
Citation Count: Khennaoui, Amina-Aicha...et al. (2021). "HYPERCHAOTIC DYNAMICS of A NEW FRACTIONAL DISCRETE-TIME SYSTEM", Fractals, Vol. 29, No. 8.
HYPERCHAOTIC DYNAMICS of A NEW FRACTIONAL DISCRETE-TIME SYSTEM
(2021) Khennaoui, Amina-Aicha; Ouannas, Adel; Momani, Shaher; Dibi, Zohir; Grassi, Giuseppe; Baleanu, Dumitru; Pham, Viet-Thanh; 56389
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 C0 complexity. Simulation results confirm the effectiveness of the approach illustrated herein. © 2021 The Author(s).