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A novel memristor-coupled hyperchaotic map: dynamical analysis, linear transform control and encryption application

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Abstract

Continuous memristors have been widely used in various chaotic circuits as well as neuromorphic circuits, but there is a relative lack of research on discrete memristors. In this paper, a new three-dimensional memristor hyperchaotic map is proposed by coupling the discrete memristor with a simple two-dimensional map. The fixed points of the map are analysed and the dynamical behaviour of the typical parameters of the map and the initial boosting is investigated using numerical simulations. For practical engineering needs, offset boosting and amplitude control of the map are performed without destroying the basic structure of the map. Finally, a simple image encryption algorithm is designed using this three-dimensional memristor hyperchaotic mapping, which has been verified to be well randomized.

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Data availability statement

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request. The manuscript has associated data in a data repository

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos.62061014); Technological innovation projects in the field of artificial intelligence in Liaoning province (Grant Nos. 2023JH26/10300011); Basic scientific research projects in department of education of Liaoning Province (Grant Nos. JYTZD2023021).

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Contributions

Xuan Wang designed and carried out experiments, data analyzed and manuscript wrote. Xianying Xu improved the algorithm. Yinghong Cao and Jun Mou made the theoretical guidance for this paper. All authors reviewed the manuscript.

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Correspondence to Yinghong Cao or Jun Mou.

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Wang, X., Cao, Y., Xu, X. et al. A novel memristor-coupled hyperchaotic map: dynamical analysis, linear transform control and encryption application. Eur. Phys. J. Plus 139, 480 (2024). https://doi.org/10.1140/epjp/s13360-024-05280-2

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