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Dynamics, Chaos Control, and Synchronization in a Fractional-Order Samardzija-Greller Population System with Order Lying in (0, 2)

Author

Listed:
  • A. Al-khedhairi
  • S. S. Askar
  • A. E. Matouk
  • A. Elsadany
  • M. Ghazel

Abstract

This paper demonstrates dynamics, chaos control, and synchronization in Samardzija-Greller population model with fractional order between zero and two. The fractional-order case is shown to exhibit rich variety of nonlinear dynamics. Lyapunov exponents are calculated to confirm the existence of wide range of chaotic dynamics in this system. Chaos control in this model is achieved via a novel linear control technique with the fractional order lying in (1, 2). Moreover, a linear feedback control method is used to control the fractional-order model to its steady states when . In addition, the obtained results illustrate the role of fractional parameter on controlling chaos in this model. Furthermore, nonlinear feedback synchronization scheme is also employed to illustrate that the fractional parameter has a stabilizing role on the synchronization process in this system. The analytical results are confirmed by numerical simulations.

Suggested Citation

  • A. Al-khedhairi & S. S. Askar & A. E. Matouk & A. Elsadany & M. Ghazel, 2018. "Dynamics, Chaos Control, and Synchronization in a Fractional-Order Samardzija-Greller Population System with Order Lying in (0, 2)," Complexity, Hindawi, vol. 2018, pages 1-14, September.
    • Handle: RePEc:hin:complx:6719341
    DOI: 10.1155/2018/6719341
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    Cited by:

    1. Chakraborty, Arkaprovo & Veeresha, P., 2024. "Investigating the dynamics, synchronization and control of chaos within a transformed fractional Samardzija–Greller framework," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    2. Al-khedhairi, A. & Matouk, A.E. & Khan, I., 2019. "Chaotic dynamics and chaos control for the fractional-order geomagnetic field model," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 390-401.

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