Scopus İndeksli Yayınlar Koleksiyonu

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

Browse

Filters

2011 - 2019132020 - 202610

Settings

Subject: search.filters.subject.Chaos

Search Results

Now showing 1 - 10 of 23
  • 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: 38
    Citation - Scopus: 40
    A New Application of the Fractional Logistic Map
    (Editura Acad Romane, 2016) Huang, Lan-Lan; Baleanu, Dumitru; Baleanu, Dumitru; Wu, Guo-Cheng; Zeng, Sheng-Da; Matematik
    The fractional chaotic map started to be applied in physics and engineering to properly treat some real-world phenomena. A shuffling method is proposed based on the fractional logistic map. The fractional difference order is used as a key. An image encryption scheme is designed by using the XOR operation and the security analysis is given. The obtained results demonstrate that the fractional difference order makes the encryption scheme highly secure.
  • 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 - WoS: 464
    Citation - Scopus: 528
    Discrete Fractional Logistic Map and Its Chaos
    (Springer, 2014) Baleanu, Dumitru; Wu, Guo-Cheng
    A discrete fractional logistic map is proposed in the left Caputo discrete delta's sense. The new model holds discrete memory. The bifurcation diagrams are given and the chaotic behaviors are numerically illustrated.
  • 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 - Scopus: 14
    Several Fractional Differences and Their Applications To Discrete Maps
    (L and H Scientific Publishing, LLC, 2015) Baleanu, D.; Zeng, S.-D.; Wu, G.-C.
    Several definitions of fractional differences are discussed. Their applications to fractional maps are compared. As an example, the logistic equation of integer order is discretized by these fractional difference methods. The comparative results show that the discrete fractional calculus is an efficient tool and the maps derived in this way have simpler forms but hold rich dynamical behaviors. © 2015 L & H Scientific Publishing, LLC.
  • Article
    Citation - WoS: 6
    Citation - Scopus: 7
    Reprint Of: Chaos Synchronization of the Discrete Fractional Logistic Map
    (Elsevier, 2015) Baleanu, Dumitru; Wu, Guo-Cheng
    In this paper, master slave synchronization for the fractional difference equation is studied with a nonlinear coupling method. The numerical simulation shows that the designed synchronization method can effectively synchronize the fractional logistic map. The Caputo-like delta derivative is adopted as the difference operator. (C) 2014 Elsevier B.V. All rights reserved.
  • 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.