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Coupled Discrete Fractional-Order Logistic Maps

Author

Listed:
  • Marius-F. Danca

    (Romanian Institute of Science and Technology, 400504 Cluj-Napoca, Romania)

  • Michal Fečkan

    (Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, 84215 Bratislava, Slovakia
    Mathematical Institute, Slovak Academy of Sciences, 84104 Bratislava, Slovakia)

  • Nikolay Kuznetsov

    (Mathematics and Mechanics Faculty, Saint-Petersburg State University, 199034 Saint Petersburg, Russia
    Department of Mathematical Information Technology, University of Jyväskylä, 40014 Jyväskylä, Finland)

  • Guanrong Chen

    (Department of Electronic Engineering, City University of Hong Kong, Hong Kong, China)

Abstract

This paper studies a system of coupled discrete fractional-order logistic maps, modeled by Caputo’s delta fractional difference, regarding its numerical integration and chaotic dynamics. Some interesting new dynamical properties and unusual phenomena from this coupled chaotic-map system are revealed. Moreover, the coexistence of attractors, a necessary ingredient of the existence of hidden attractors, is proved and analyzed.

Suggested Citation

  • Marius-F. Danca & Michal Fečkan & Nikolay Kuznetsov & Guanrong Chen, 2021. "Coupled Discrete Fractional-Order Logistic Maps," Mathematics, MDPI, vol. 9(18), pages 1-14, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:18:p:2204-:d:631509
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    References listed on IDEAS

    as
    1. López-Ruiz, Ricardo & Fournier-Prunaret, Danièle, 2005. "Indirect Allee effect, bistability and chaotic oscillations in a predator–prey discrete model of logistic type," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 85-101.
    2. I. Area & J. Losada & J. J. Nieto, 2014. "On Fractional Derivatives and Primitives of Periodic Functions," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, August.
    3. Danca, Marius-F., 2021. "Hopfield neuronal network of fractional order: A note on its numerical integration," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    4. Santanu Saha Ray & Abdon Atangana & S. C. Oukouomi Noutchie & Muhammet Kurulay & Necdet Bildik & Adem Kilicman, 2014. "Fractional Calculus and Its Applications in Applied Mathematics and Other Sciences," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-2, December.
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    Cited by:

    1. Ma, Tao & Mou, Jun & Banerjee, Santo & Cao, Yinghong, 2023. "Analysis of the functional behavior of fractional-order discrete neuron under electromagnetic radiation," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    2. Michal Fečkan & Marius-F. Danca, 2022. "Stability, Periodicity, and Related Problems in Fractional-Order Systems," Mathematics, MDPI, vol. 10(12), pages 1-2, June.

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