Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Now showing 1 - 6 of 6
  • Article
    Citation - WoS: 3
    Citation - Scopus: 4
    Hyperchaotic Dynamics of a New Fractional Discrete-Time System
    (World Scientific Publ Co Pte Ltd, 2021) Ouannas, Adel; Momani, Shaher; Dibi, Zohir; Grassi, Giuseppe; Baleanu, Dumitru; Viet-Thanh Pham; Khennaoui, Amina-Aicha; Pham, Viet-Thanh
    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.
  • Article
    Citation - WoS: 98
    Citation - Scopus: 121
    A Nonstandard Finite Difference Scheme for the Modeling and Nonidentical Synchronization of a Novel Fractional Chaotic System
    (Springer, 2021) Baleanu, D.; Zibaei, S.; Namjoo, M.; Jajarmi, A.
    The aim of this paper is to introduce and analyze a novel fractional chaotic system including quadratic and cubic nonlinearities. We take into account the Caputo derivative for the fractional model and study the stability of the equilibrium points by the fractional Routh–Hurwitz criteria. We also utilize an efficient nonstandard finite difference (NSFD) scheme to implement the new model and investigate its chaotic behavior in both time-domain and phase-plane. According to the obtained results, we find that the new model portrays both chaotic and nonchaotic behaviors for different values of the fractional order, so that the lowest order in which the system remains chaotic is found via the numerical simulations. Afterward, a nonidentical synchronization is applied between the presented model and the fractional Volta equations using an active control technique. The numerical simulations of the master, the slave, and the error dynamics using the NSFD scheme are plotted showing that the synchronization is achieved properly, an outcome which confirms the effectiveness of the proposed active control strategy. © 2021, The Author(s).
  • Article
    Citation - WoS: 5
    Citation - Scopus: 11
    Bifurcations, Hidden Chaos and Control in Fractional Maps
    (Mdpi, 2020) Almatroud, Othman Abdullah; Khennaoui, Amina Aicha; Alsawalha, Mohammad Mossa; Baleanu, Dumitru; Van Van Huynh; Viet-Thanh Pham; Ouannas, Adel; Pham, Viet-thanh; Huynh, Van Van
    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.
  • Article
    Citation - WoS: 37
    Citation - Scopus: 63
    Chaotic Incommensurate Fractional Order Rossler System: Active Control and Synchronization
    (Springer, 2011) Majd, Vahid Johari; Baleanu, Dumitru; Razminia, Abolhassan
    In this article, we present an active control methodology for controlling the chaotic behavior of a fractional order version of Rossler system. The main feature of the designed controller is its simplicity for practical implementation. Although in controlling such complex system several inputs are used in general to actuate the states, in the proposed design, all states of the system are controlled via one input. Active synchronization of two chaotic fractional order Rossler systems is also investigated via a feedback linearization method. In both control and synchronization, numerical simulations show the efficiency of the proposed methods.
  • Article
    Citation - WoS: 47
    Citation - Scopus: 55
    Transient Chaos in Fractional Bloch Equations
    (Pergamon-elsevier Science Ltd, 2012) Daftardar-Gejji, Varsha; Baleanu, Dumitru; Magin, Richard; Bhalekar, Sachin
    The Bloch equation provides the fundamental description of nuclear magnetic resonance (NMR) and relaxation (T-1 and T-2). This equation is the basis for both NMR spectroscopy and magnetic resonance imaging (MRI). The fractional-order Bloch equation is a generalization of the integer-order equation that interrelates the precession of the x, y and z components of magnetization with time- and space-dependent relaxation. In this paper we examine transient chaos in a non-linear version of the Bloch equation that includes both fractional derivatives and a model of radiation damping. Recent studies of spin turbulence in the integer-order Bloch equation suggest that perturbations of the magnetization may involve a fading power law form of system memory, which is concisely embedded in the order of the fractional derivative. Numerical analysis of this system shows different patterns in the stability behavior for alpha near 1.00. In general, when alpha is near 1.00, the system is chaotic, while for 0.98 >= alpha >= 0.94, the system shows transient chaos. As the value of alpha decreases further, the duration of the transient chaos diminishes and periodic sinusoidal oscillations emerge. These results are consistent with studies of the stability of both the integer and the fractional-order Bloch equation. They provide a more complete model of the dynamic behavior of the NMR system when non-linear feedback of magnetization via radiation damping is present. (C) 2012 Elsevier Ltd. All rights reserved.
  • Article
    Citation - WoS: 39
    Citation - Scopus: 48
    Chaotic Attractors With Fractional Conformable Derivatives in the Liouville-Caputo Sense and Its Dynamical Behaviors
    (Mdpi, 2018) Baleanu, Dumitru; Tchier, Fairouz; Solis Perez, Jesus Emmanuel; Francisco Gomez-Aguilar, Jose; Gómez-Aguilar, José Francisco; Pérez, Jesús Emmanuel Solís
    This paper deals with a numerical simulation of fractional conformable attractors of type Rabinovich-Fabrikant, Thomas' cyclically symmetric attractor and Newton-Leipnik. Fractional conformable and beta-conformable derivatives of Liouville-Caputo type are considered to solve the proposed systems. A numerical method based on the Adams-Moulton algorithm is employed to approximate the numerical simulations of the fractional-order conformable attractors. The results of the new type of fractional conformable and beta-conformable attractors are provided to illustrate the effectiveness of the proposed method.