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Multistability, chaos and hyperchaos in a novel 3D discrete memristive system: microcontroller implementation and cryptography

  • Brondelle Falonne Namekong Tatang , Adele Armele Ngo Mouelas , Rodrigue Andre Tchamda , Herman Landry Ndassi , Romanic Kengne EMAIL logo and Martin Tchoffo
Published/Copyright: April 22, 2025
Zeitschrift für Naturforschung A
From the journal Zeitschrift für Naturforschung A Volume 80 Issue 6

Abstract

Discrete nonlinear systems involving memristors have been extensively studied in recent years. In this work, we combine the nonlinearity of a discrete memristor with a sinusoidal transformation scheme to construct a new 3D discrete hyperchaotic circuit, which is useful for image encryption. Firstly, we perform a dynamical analysis of the proposed system. Using analytical and numerical tools, we find that the model exhibits rich and complex dynamics, including fixed-point planes, hidden attractors, hyperchaos, periodicity, and multistability. To demonstrate its practical implementation, the proposed oscillator is integrated into a microcontroller-based laboratory setup, and the experimental results closely match the numerical findings. Secondly, hyperchaotic sequences generated by the new model are used to build a simple 8 × 8 S-box for secure image encryption. The hyperchaotic sequences are first used to shuffle the columns and rows of the original image, which is then substituted using the 8 × 8 substitution box and finally encrypted through nonlinear diffusion. To validate the performance of our protocol, we conduct standard security analyses, including correlation coefficient evaluation, pixel change rate, information entropy, time complexity, and key space analysis. The results are in perfect agreement with those in the literature.

Keywords: discrete system; memristor; microcontroller implementation; image encryption; substitution box
Corresponding author: Romanic Kengne, Laboratory of Condensed Matter, Electronics and Signal Processing, Department of Physics, Faculty of Sciences, University of Dschang, P.O. Box 67, Dschang, Cameroon, E-mail: 

Acknowledgments

The authors express their gratitude to Pr. Robert Tchitnga for his advice during the working out of this manuscript.

  1. Research ethics: Not applicable.

  2. Informed consent: Not Applicable.

  3. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission. R.K and M.T built the problem and proposed the model. B.N.T and A.A.N.M dealt with the stability and perform numerical simulation. B.N.T, A.A.N.M and H.L.N dealt with the cryptography. A.R.T dealt with the microcontroller implementation. B.N.T and A.A.N.M revised the manuscript.

  4. Use of Large Language Models, AI and Machine Learning Tools: None declared.

  5. Conflict of interest: All other authors state no conflict of interest.

  6. Research funding: None declared.

  7. Data availability: None declared.

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Received: 2025-01-19
Accepted: 2025-03-20
Published Online: 2025-04-22
Published in Print: 2025-06-26

© 2025 Walter de Gruyter GmbH, Berlin/Boston

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  2. Dynamical Systems & Nonlinear Phenomena
  3. Controlling the convective heat transfer of shear thinning and shear thickening fluids in parallel plates with magnetic force
  4. Multistability, chaos and hyperchaos in a novel 3D discrete memristive system: microcontroller implementation and cryptography
  5. Comparative study of thermally intense cilia and non-cilia generated motion of Ellis’s fluid by using MATHEMATICA 14.1
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https://doi.org/10.1515/zna-2025-0024
Keywords for this article
discrete system; memristor; microcontroller implementation; image encryption; substitution box

Articles in the same Issue

  1. Frontmatter
  2. Dynamical Systems & Nonlinear Phenomena
  3. Controlling the convective heat transfer of shear thinning and shear thickening fluids in parallel plates with magnetic force
  4. Multistability, chaos and hyperchaos in a novel 3D discrete memristive system: microcontroller implementation and cryptography
  5. Comparative study of thermally intense cilia and non-cilia generated motion of Ellis’s fluid by using MATHEMATICA 14.1
  6. Fundamental Concepts of Physical Science
  7. Nonlinear electrodynamics and its possible connection to relativistic superconductivity: instance of a time-dependent system
  8. Galilean decoherence and quantum measurement
  9. Solid State Physics & Materials Science
  10. A dynamically tunable polarization-insensitive broadband vanadium dioxide-assisted absorber for terahertz applications
  11. Thermodynamics & Statistical Physics
  12. Heat transfer analysis for the Cattaneo–Cristov heat flux model using integral transform technique with isothermal and isoflux wall conditions
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