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Dynamical study of a novel 4D hyperchaotic system: An integer and fractional order analysis

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  • Iskakova, Kulpash
  • Alam, Mohammad Mahtab
  • Ahmad, Shabir
  • Saifullah, Sayed
  • Akgül, Ali
  • Yılmaz, Gülnur

Abstract

In this article, a new nonlinear four-dimensional hyperchaotic model is presented. The dynamical aspects of the complex system are analyzed covering equilibrium points, linear stability, dissipation, bifurcations, Lyapunov exponent, phase portraits, Poincaré mapping, attractor projection, sensitivity and time series analysis. To analyze hidden attractors, the proposed system is investigated through nonlocal operator in Caputo sense. The existence of solution of the system in fractional sense is studied by fixed point theory. The stability of fractional order system is demonstrated via Matignon stability criteria. The fractional order system is numerically studied via newly developed numerical method which is based on Newton polynomial interpolation. The evolution of the attractors are depicted with different fractional orders. For few fractional orders, some hidden strange chaotic attractors are observed through graphs. Theoretical and numerical studies demonstrate that this model has complex dynamics with some stimulating physical characteristics. To verify and validate the results, we implement Field Programmable Analog Arrays (FPAA).

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  • Iskakova, Kulpash & Alam, Mohammad Mahtab & Ahmad, Shabir & Saifullah, Sayed & Akgül, Ali & Yılmaz, Gülnur, 2023. "Dynamical study of a novel 4D hyperchaotic system: An integer and fractional order analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 219-245.
    • Handle: RePEc:eee:matcom:v:208:y:2023:i:c:p:219-245
    DOI: 10.1016/j.matcom.2023.01.024
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    1. Yinlan Chen & Haodong Zhang & Xu Kong & Ailong Wu, 2021. "A New Fractional-Order Hyperchaotic System and Its Adaptive Tracking Control," Discrete Dynamics in Nature and Society, Hindawi, vol. 2021, pages 1-9, February.
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    4. Pu, Xueke, 2015. "Dynamics of a fractional hydrodynamical equation for the Heisenberg paramagnet," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 213-229.
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    6. Yong Wu & Shabir Ahmad & Aman Ullah & Kamal Shah & Nasser Hassen Sweilam, 2022. "Study of the Fractional-Order HIV-1 Infection Model with Uncertainty in Initial Data," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-16, January.
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    Cited by:

    1. Lu, Yang & Gong, Mengxin & Gan, Zhihua & Chai, Xiuli & Cao, Lvchen & Wang, Binjie, 2023. "Exploiting one-dimensional improved Chebyshev chaotic system and partitioned diffusion based on the divide-and-conquer principle for 3D medical model encryption," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
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    3. Nikhil Pachauri & Velamuri Suresh & MVV Prasad Kantipudi & Reem Alkanhel & Hanaa A. Abdallah, 2023. "Multi-Drug Scheduling for Chemotherapy Using Fractional Order Internal Model Controller," Mathematics, MDPI, vol. 11(8), pages 1-19, April.

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