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Chaotic dynamics of fractional difference magnetic levitation model with application to image encryption

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Abstract

Magnetic levitation or Maglev technology has become exciting technology with the aim of developing advanced transportation at high speed. The article aims at investigating the nonlinear nature of the magnetic levitation model using Caputo fractional difference operator with variable order. In the context of non-linear systems, the evolution of the chaotic and complex dynamics are addressed with bifurcation diagrams and largest Lyapunov exponents for constant fractional order and time varying order. Transition of the state variables in the form of phase plane and time varying plots are presented for better understanding. Approximate entropy analysis guides our knowledge on the randomness of the chaotic time series of the magnetic levitation model. Synchronization of the driven and response systems with nonlinear control function is established. The application of the model’s chaotic nature in the process of image encryption is presented. Histogram analysis and correlation co-efficient are discussed together with the information entropy of the encrypted image.

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Acknowledgements

We would like to thank UPNM for supporting this research via Postdoctoral and postgraduate research Grant UPNM/2022/GPPP/SG/13, the Natural Science Foundation of China (no. 61901530) and the Natural Science Foundation of Hunan Province (no. 2020JJ5767).

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The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

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Author notes

  1. Shaobo He and N. A. A. Fataf contributed equally to this work.

Authors and Affiliations

  1. Cyber Security and Digital Industrial Revolution Centre, Universiti Pertahanan Nasional Malaysia, Kem, Sungai Besi, Kuala Lumpur, 57000, Malaysia

    D. Vignesh & N. A. A. Fataf

  2. Centre for Defence Foundation Studies, Universiti Pertahanan Nasional Malaysia, Kem, Sungai Besi, Kuala Lumpur, 57000, Malaysia

    D. Vignesh & N. A. A. Fataf

  3. School of Automation and Electronic Information, Xiangtan University, Xiangtan, 411105, China

    Shaobo He

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  1. D. Vignesh
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All authors contributed equally to the study conception and design. All authors read and approved the final manuscript.

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Correspondence to D. Vignesh.

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Vignesh, D., He, S. & Fataf, N.A.A. Chaotic dynamics of fractional difference magnetic levitation model with application to image encryption. Eur. Phys. J. Spec. Top. 232, 2675–2691 (2023). https://doi.org/10.1140/epjs/s11734-023-00917-2

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