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Hidden attractors in fractional-order discrete maps

Author

Listed:
  • Vaibhav Varshney

    (University of Delhi)

  • S. Leo Kingston

    (Lodz University of Technology
    SRM Institute of Science and Technology)

  • Sabarathinam Srinivasan

    (Saveetha University)

  • Suresh Kumarasamy

    (Easwari Engineering College)

Abstract

This study investigates the hidden dynamics of fractional-order discrete two-dimensional maps, focusing on the generation of hidden attractors and the impact of order on their size and boundaries. Three different nonlinear maps are used, and various measures, such as phase portraits, bifurcation diagrams, and basin of attraction, are presented. This study also observes changes in basin boundaries of hidden attractors with varying order. The rational memristive maps exhibit a well-defined basin of attraction for a broad range of system orders, with multistability and a riddled basin for some orders. The memristive Gauss map also shows well-defined and riddled basins, however, the quadratic chaotic map demonstrates a decreasing basin size and a riddled basin boundary for higher orders of the system. Graphic abstract

Suggested Citation

  • Vaibhav Varshney & S. Leo Kingston & Sabarathinam Srinivasan & Suresh Kumarasamy, 2024. "Hidden attractors in fractional-order discrete maps," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(10), pages 1-10, October.
    • Handle: RePEc:spr:eurphb:v:97:y:2024:i:10:d:10.1140_epjb_s10051-024-00780-7
    DOI: 10.1140/epjb/s10051-024-00780-7
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    References listed on IDEAS

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    1. Karthikeyan Rajagopal & Shirin Panahi & Mo Chen & Sajad Jafari & Bocheng Bao, 2021. "Suppressing Spiral Wave Turbulence In A Simple Fractional-Order Discrete Neuron Map Using Impulse Triggering," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(08), pages 1-10, December.
    2. Palanivel, J. & Suresh, K. & Sabarathinam, S. & Thamilmaran, K., 2017. "Chaos in a low dimensional fractional order nonautonomous nonlinear oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 33-41.
    3. Xu, Quan & Lin, Yi & Bao, Bocheng & Chen, Mo, 2016. "Multiple attractors in a non-ideal active voltage-controlled memristor based Chua's circuit," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 186-200.
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