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Numerical Analysis For Hidden Chaotic Behavior Of A Coupled Memristive Dynamical System Via Fractal–Fractional Operator Based On Newton Polynomial Interpolation

Author

Listed:
  • SHAIMAA A. M. ABDELMOHSEN

    (Department of Physics, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

  • SHABIR AHMAD

    (��Department of Mathematics, University of Malakand, Chakdara, Dir Lower, Khyber Pakhtunkhwa, Pakistan)

  • MANSOUR F. YASSEN

    (��Department of Mathematics, College of Science and Humanities in Al-Aflaj, Prince Sattam Bin Abdulaziz University, Al-Aflaj 11912, Saudi Arabia§Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Damietta, Egypt)

  • SAEED AHMED ASIRI

    (�Mechanical Engineering Department, Engineering College, King Abdulaziz University, Jeddah, Saudi Arabia)

  • ABDELBACKI M. M. ASHRAF

    (��Plant Pathology Department, Faculty of Agriculture, Cairo University, Giza 12613, Egypt)

  • SAYED SAIFULLAH

    (��Department of Mathematics, University of Malakand, Chakdara, Dir Lower, Khyber Pakhtunkhwa, Pakistan)

  • FAHD JARAD

    (*Department of Mathematics, Cankaya University, Etimesgut 06790, Ankara, Turkey††Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia‡‡Department of Medical Research, China Medical University, Taichung 40402, Taiwan, R. O. China)

Abstract

Dynamical features of a coupled memristive chaotic system have been studied using a fractal–fractional derivative in the sense of Atangana–Baleanu. Dissipation, Poincaré section, phase portraits, and time-series behaviors are all examined. The dissipation property shows that the suggested system is dissipative as long as the parameter g > 0. Similarly, from the Poincaré section it is observed that, lowering the value of the fractal dimension, an asymmetric attractor emerges in the system. In addition, fixed point notions are used to analyze the existence and uniqueness of the solution from a fractal–fractional perspective. Numerical analysis using the Adams–Bashforth method which is based on Newton’s Polynomial Interpolation is performed. Furthermore, multiple projections of the system with different fractional orders and fractal dimensions are quantitatively demonstrated, revealing new characteristics in the proposed model. The coupled memristive system exhibits certain novel, strange attractors and behaviors that are not observable by the local operators.

Suggested Citation

  • Shaimaa A. M. Abdelmohsen & Shabir Ahmad & Mansour F. Yassen & Saeed Ahmed Asiri & Abdelbacki M. M. Ashraf & Sayed Saifullah & Fahd Jarad, 2023. "Numerical Analysis For Hidden Chaotic Behavior Of A Coupled Memristive Dynamical System Via Fractal–Fractional Operator Based On Newton Polynomial Interpolation," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(10), pages 1-22.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:10:n:s0218348x2340087x
    DOI: 10.1142/S0218348X2340087X
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