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An improved Hénon map based on G-L fractional-order discrete memristor and its FPGA implementation

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Abstract

In recent years, the application of memristors in the field of chaos has become a research hotspot. Researchers have employed integer-order discrete memristors into Hénon maps, and analyzed its characteristics. In this paper, a fractional-order discrete memristor (FDM) based on Grunwald-Letnikov definition is introduced, and it is proved that it meets the definition of generalized memristor. The FDM is applied to Hénon map and an improved Hénon map is designed. Its dynamics is analyzed by attractors, bifurcation diagrams, maximum Lyapunov exponent spectrum and permutation entropy complexity. The results show that the improved map has a wider chaos range than the original Hénon map and integer-order discrete memristive Hénon map, and the order affects the state of the system and is one of the bifurcation parameters. Finally, we implement the improved Hénon map on FPGA platform.

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Data Availibility Statement

This manuscript has associated data in a data repository. [Authors’ comment: The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant Nos. 62061008, 62071496, 61901530).

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Authors and Affiliations

  1. School of Electronic Information, Central South University, Changsha, 410083, China

    Huihai Wang & Guang Li

  2. School of Physics, Central South University, Changsha, 410083, China

    Kehui Sun

  3. School of Automation and Electronic Information, Xiangtan University, Xiangtan, 411105, China

    Shaobo He

Authors
  1. Huihai Wang
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  2. Guang Li
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  4. Shaobo He
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Correspondence to Shaobo He.

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Wang, H., Li, G., Sun, K. et al. An improved Hénon map based on G-L fractional-order discrete memristor and its FPGA implementation. Eur. Phys. J. Plus 139, 154 (2024). https://doi.org/10.1140/epjp/s13360-024-04924-7

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