https://doi.org/10.1140/epjs/s11734-023-00917-2
Regular Article
Chaotic dynamics of fractional difference magnetic levitation model with application to image encryption
1
Cyber Security and Digital Industrial Revolution Centre, Universiti Pertahanan Nasional Malaysia, Kem, Sungai Besi, 57000, Kuala Lumpur, Malaysia
2
Centre for Defence Foundation Studies, Universiti Pertahanan Nasional Malaysia, Kem, Sungai Besi, 57000, Kuala Lumpur, Malaysia
3
School of Automation and Electronic Information, Xiangtan University, 411105, Xiangtan, China
Received:
17
March
2023
Accepted:
2
July
2023
Published online:
2
August
2023
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.
Shaobo He and N. A. A. Fataf contributed equally to this work.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
