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A new four-dimensional memristive system, synchronization and its application in image encryption

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Abstract

In this paper, a new four-dimensional (4D) memristive system is presented by introducing a memristor equation to a 3D chaotic system. Firstly, the basic characteristics including existence and stability of equilibrium points, and Kaplan–Yoke dimension for the memristive system are analyzed from a theoretical perspective. The description of the 4D memristive system in the integer-order and the fractional-order cases is given. In both cases, the dynamics with the variation of a system parameter or a derivative order is studied by the numerical simulations. The results show that the integer-order and the fractional-order memristive systems have rich dynamics. Secondly, in order to realize the synchronization for the memristive system, two adaptive synchronization schemes are designed, namely, the identical structure and the different structure synchronization. Numerical simulation results show that the designed synchronization controllers are effective. Finally, a novel image encryption algorithm is expanded to the image encryption for color images based on the memristive system. The simulation results demonstrate the image encryption method based on the memristive system has a perfect encryption effect for the color images.

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Data availability

The datasets generated and analyzed during the current study are available from the corresponding author on reasonable request.

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Funding

This study was funded by the National Natural Science Foundation of Shaanxi province (No. 2023-JC-YB-075) and the Natural Science Preparatory Study Foundation of **’an University of Posts and Telecommunications (No.106/205020030).

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Authors and Affiliations

  1. School of Sciences, **’an University of Posts and Telecommunications, **’an, 710061, China

    **aojun Liu, Pu Wang & **g Tian

  2. School of Automation, **’an University of Posts and Telecommunications, **’an, 710061, China

    Dafeng Tang

Authors
  1. **aojun Liu
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  2. Pu Wang
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  3. Dafeng Tang
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  4. **g Tian
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Contributions

Funding acquisition, investigation, writing, and original draft preparation by **aojun Liu; software, data analysis, and formal analysis by Pu Wang; methodology, writing, and editing by Dafeng Tang and **g Tian.

Corresponding author

Correspondence to **aojun Liu.

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The code will be made available on request.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Liu, X., Wang, P., Tang, D. et al. A new four-dimensional memristive system, synchronization and its application in image encryption. Int. J. Dynam. Control (2024). https://doi.org/10.1007/s40435-024-01464-x

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  • DOI: https://doi.org/10.1007/s40435-024-01464-x

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