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Time-Delay Synchronization and Anti-Synchronization of Variable-Order Fractional Discrete-Time Chen–Rossler Chaotic Systems Using Variable-Order Fractional Discrete-Time PID Control

Author

Listed:
  • Joel Perez Padron

    (The Dynamical Systems Group, Department of Physical and Mathematical Sciences, Universidad Autónoma de Nuevo León, San Nicolás de los Garza 66451, NL, Mexico)

  • Jose Paz Perez

    (The Dynamical Systems Group, Department of Physical and Mathematical Sciences, Universidad Autónoma de Nuevo León, San Nicolás de los Garza 66451, NL, Mexico)

  • José Javier Pérez Díaz

    (Department of Mechanical and Electrical Engineering, Universidad Autónoma de Nuevo León, San Nicolás de los Garza 66451, NL, Mexico)

  • Atilano Martinez Huerta

    (The Dynamical Systems Group, Department of Physical and Mathematical Sciences, Universidad Autónoma de Nuevo León, San Nicolás de los Garza 66451, NL, Mexico)

Abstract

In this research paper, we solve the problem of synchronization and anti-synchronization of chaotic systems described by discrete and time-delayed variable fractional-order differential equations. To guarantee the synchronization and anti-synchronization, we use the well-known PID (Proportional-Integral-Derivative) control theory and the Lyapunov–Krasovskii stability theory for discrete systems of a variable fractional order. We illustrate the results obtained through simulation with examples, in which it can be seen that our results are satisfactory, thus achieving synchronization and anti-synchronization of chaotic systems of a variable fractional order with discrete time delay.

Suggested Citation

  • Joel Perez Padron & Jose Paz Perez & José Javier Pérez Díaz & Atilano Martinez Huerta, 2021. "Time-Delay Synchronization and Anti-Synchronization of Variable-Order Fractional Discrete-Time Chen–Rossler Chaotic Systems Using Variable-Order Fractional Discrete-Time PID Control," Mathematics, MDPI, vol. 9(17), pages 1-15, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2149-:d:628499
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    References listed on IDEAS

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    1. Hai-Peng Jiang & Yong-Qiang Liu, 2016. "Disturbance Rejection for Fractional-Order Time-Delay Systems," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-8, July.
    2. Dominik Sierociuk & Wiktor Malesza, 2017. "Fractional variable order discrete-time systems, their solutions and properties," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(14), pages 3098-3105, October.
    3. Weiwei Zhang & Jinde Cao & Ahmed Alsaedi & Fuad Eid S. Alsaadi, 2017. "Synchronization of Time Delayed Fractional Order Chaotic Financial System," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-5, October.
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    Cited by:

    1. Priyanka, K. Sri Raja & Soundararajan, G. & Kashkynbayev, Ardak & Nagamani, G., 2023. "Exponential H∞ synchronization and anti-synchronization of delayed discrete-time complex-valued neural networks with uncertainties," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 301-321.
    2. M. Hymavathi & Tarek F. Ibrahim & M. Syed Ali & Gani Stamov & Ivanka Stamova & B. A. Younis & Khalid I. Osman, 2022. "Synchronization of Fractional-Order Neural Networks with Time Delays and Reaction-Diffusion Terms via Pinning Control," Mathematics, MDPI, vol. 10(20), pages 1-18, October.

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