Scopus İndeksli Yayınlar Koleksiyonu

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

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Start date: 2020Subject: search.filters.subject.Chaos

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  • Article
    Nonlinear Dynamics and Chaos in Fractional-Order Cardiac Action Potential Duration Mapping Model
    (Global Science Press, 2026) Bououden, Rabah; Abdelouahab, Mohammed S.; Houmor, Tarek; Jarad, Fahd
  • Article
    Bifurcations, Hidden Chaos and Control in Fractional Maps
    (MDPI AG, 2020) Pham, Viet-Thanh; Ouannas, Adel; Almatroud, Othman Abdullah; Baleanu, Dumitru; Alsawalha, Mohammad Mossa; Khennaoui, Amina Aicha; Huynh, Van Van
  • Article
    Citation - WoS: 41
    Citation - Scopus: 44
    Nonlinear Dynamics and Chaos in Fractional Differential Equations With a New Generalized Caputo Fractional Derivative
    (Elsevier, 2022) Baleanu, Dumitru; Odibat, Zaid
    In this paper, novel systems of fractional differential equations involving a new generalized Caputo fractional derivative were proposed. The complex dynamic behavior of these systems was studied by numerical simulation. Nonlinear dynamics and chaos in hybrid fractional order systems were investigated using a predictor-corrector algorithm. In particular, the effect of the new generalized fractional derivative parameters on the dynamics of the proposed systems was discussed. The rich variation obtained from the characteristics of the studied systems recommends the implementation of the new generalized derivative in fractional calculus applications.
  • Article
    Citation - Scopus: 20
    Applications of Short Memory Fractional Differential Equations With Impulses
    (L and H Scientific Publishing, LLC, 2023) Wu, G.-C.; Baleanu, D.; Shiri, B.
    Dynamical systems’ behavior is sometimes varied with some impulse and sudden changes in process. The dynamics of these systems can not be modeled by previous concepts of derivative or fractional derivatives any longer. The short memory concept is a solution and a better choice for fractional modeling of such processes. We apply short memory fractional differential equations for these systems. We propose collocation methods based on piecewise polynomials to approximate solutions of these equations. We provide various examples to demonstrate the application of the short memory derivative for impulse systems and efficiency of the presented numerical methods. © 2023 L&H Scientific Publishing, LLC. All rights reserved
  • Article
    Citation - WoS: 3
    Citation - Scopus: 5
    Simpson's Method for Fractional Differential Equations With a Non-Singular Kernel Applied To a Chaotic Tumor Model
    (Iop Publishing Ltd, 2021) Defterli, Ozlem; Tang, Yifa; Baleanu, Dumitru; Arshad, Sadia; Saleem, Iram
    This manuscript is devoted to describing a novel numerical scheme to solve differential equations of fractional order with a non-singular kernel namely, Caputo-Fabrizio. First, we have transformed the fractional order differential equation to the corresponding integral equation, then the fractional integral equation is approximated by using the Simpson's quadrature 3/8 rule. The stability of the proposed numerical scheme and its convergence is analyzed. Further, a cancer growth Caputo-Fabrizio model is solved using the newly proposed numerical method. Moreover, the numerical results are provided for different values of the fractional-order within some special cases of model parameters.
  • Article
    Citation - WoS: 99
    Citation - Scopus: 101
    Quasi-Periodic, Chaotic and Travelling Wave Structures of Modified Gardner Equation
    (Pergamon-elsevier Science Ltd, 2021) Hussain, Amjad; Junaid-U-Rehman, M.; Baleanu, Dumitru; Riaz, Muhammad Bilal; Jhangeer, Adil
    In this paper, the nonlinear modified Gardner (mG) equation is under consideration which represents the super nonlinear proliferation of the ion-acoustic waves and quantum electron-positronion magneto plasmas. The considered model is investigated with the help of Lie group analysis. Lie point symmetries are computed under the invariance criteria of Lie groups and symmetry group for each generator is reported. Furthermore, the one-dimensional optimal system of subalgebras is developed by adjoint technique and then we compute the similarity reductions corresponding to each vector field present in the optimal system, with the help of similarity reduction method we have to convert the PDE into the ODE. Some exact explicit solutions of obtained ordinary differential equations were constructed by the power series technique. With the aid of the Galilean transformation, the model is transformed into a planer dynamical system and the bifurcation behaviour is recorded. All practicable types of phase portraits with regard to the parameters of the problem considered are plotted. Meantime, sensitivity is observed by utilizing sensitivity analysis. In addition, the influence of physical parameters is studied by the application of an extrinsic periodic power. With additional perturbed term, quasi-periodic and quasi-periodic-chaotic behaviours is reported. (c) 2021 Elsevier Ltd. All rights reserved.
  • Article
    Citation - WoS: 165
    Citation - Scopus: 190
    Numerical Simulation of Initial Value Problems With Generalized Caputo-Type Fractional Derivatives
    (Elsevier, 2020) Baleanu, Dumitru; Odibat, Zaid
    We introduce a new generalized Caputo-type fractional derivative which generalizes Caputo fractional derivative. Some characteristics were derived to display the new generalized derivative features. Then, we present an adaptive predictor corrector method for the numerical solution of generalized Caputo-type initial value problems. The proposed algorithm can be considered as a fractional extension of the classical Adams-Bashforth-Moulton method. Dynamic behaviors of some fractional derivative models are numerically discussed. We believe that the presented generalized Caputo-type fractional derivative and the proposed algorithm are expected to be further used to formulate and simulate many generalized Caputo type fractional models. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.
  • 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.