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

• Published in: The European physical journal. ST, Special topics Vol. 232; no. 14-15; pp. 2675 - 2691
• Main Authors: Vignesh, D., He, Shaobo, Fataf, N. A. A.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-11-2023; Springer Nature B.V
• Subjects: Atomic; Classical and Continuum Physics; Condensed Matter Physics; Encryption; Entropy (Information theory); Finite differences; Liapunov exponents; Magnetic levitation; Materials Science; Measurement Science and Instrumentation; Molecular; Nonlinear control; Nonlinear systems; Operators (mathematics); Optical and Plasma Physics; Physics; Physics and Astronomy; Recent Advancement of Fractional-Calculus and Its Applications in Physical Systems; Regular Article; Synchronism
• ISSN: 1951-6355; 1951-6401
• DOI: 10.1140/epjs/s11734-023-00917-2

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.