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Theoretical And Numerical Investigation Of Complexities In Fractional-Order Chaotic System Having Torus Attractors

Author

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  • CHANGJIN XU

    (Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang 550025, P. R. China†Guizhou Key Laboratory of Big Data Statistical Analysis, Guiyang 550025, P. R. China)

  • MATI UR RAHMAN

    (��School of Mathematical Science, Shanghai Jiao Tong University, Shanghai, P. R. China)

  • BIBI FATIMA

    (�Department of Mathematics, University of Malakand, KPK, Pakistan)

  • YELÄ°Z KARACA

    (�University of Massachusetts Medical School (UMASS), Worcester, MA 01655, USA)

Abstract

This paper presents a theoretical and complex numerical analysis of the 2-torus chaotic system with a power-law kernel. Various dynamical characteristics of the complex system are investigated covering existence uniqueness, attractor projection, time series analysis and sensitivity towards initial values. 4-torus attractor coexistence is observed with different fractional orders. The numerical scheme is used to approximate the system numerically which is based on the Newton polynomials. The numerical illustrations of the system demonstrate that moving from higher fractional-order to lower fractional-order affects the dynamics of the system significantly, which in turn has a shrinking impact on the geometry of the oscillatory range. The emergence of new oscillations can also be observed at lower fractional orders, revealing that the system oscillates rapidly with lower amplitudes as compared to those having higher fractional orders.

Suggested Citation

  • Changjin Xu & Mati Ur Rahman & Bibi Fatima & Yelä°Z Karaca, 2022. "Theoretical And Numerical Investigation Of Complexities In Fractional-Order Chaotic System Having Torus Attractors," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(07), pages 1-13, November.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:07:n:s0218348x2250164x
    DOI: 10.1142/S0218348X2250164X
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