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Numerical Simulation Of The Fractional-Order Rã–Ssler Chaotic Systems With Grãœnwald–Letnikov Fractional Derivative

Author

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  • XIAOYU LI

    (College of Science, Inner Mongolia University of Technology, Hohhot 010051, P. R. China‡College of Date Science and Application, Inner Mongolia University of Technology, Hohhot 010080, P. R. China)

  • YU-LAN WANG

    (College of Science, Inner Mongolia University of Technology, Hohhot 010051, P. R. China†Department of Mathematics, Inner Mongolia University of Technology, Hohhot 010051, P. R. China)

Abstract

In recent years, scholars have studied the chaotic behavior in the fractional dynamic systems and found that the fractional dynamic systems have unique properties that the integer dynamic systems do not have. Therefore, the numerical simulation of fractional chaotic systems is very important. This paper introduces a high-precision numerical method for the fractional-order Rössler chaotic systems. Complex dynamic behavior of the fractional-order Rössler chaotic systems is shown by using the present method. We observe some novel dynamic behaviors in numerical simulation which are unlike any that have been previously found in numerical experiments or theoretical studies. The simulation results of numerical experiments demonstrate the effectiveness of the present method.

Suggested Citation

  • Xiaoyu Li & Yu-Lan Wang, 2022. "Numerical Simulation Of The Fractional-Order Rã–Ssler Chaotic Systems With Grãœnwald–Letnikov Fractional Derivative," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(08), pages 1-8, December.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:08:n:s0218348x22402290
    DOI: 10.1142/S0218348X22402290
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    Cited by:

    1. Bukhari, Ayaz Hussain & Raja, Muhammad Asif Zahoor & Alquhayz, Hani & Abdalla, Manal Z.M. & Alhagyan, Mohammed & Gargouri, Ameni & Shoaib, Muhammad, 2023. "Design of intelligent hybrid NAR-GRNN paradigm for fractional order VDP chaotic system in cardiac pacemaker with relaxation oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).

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