https://doi.org/10.1140/epjp/s13360-024-04924-7
Regular Article
An improved Hénon map based on G-L fractional-order discrete memristor and its FPGA implementation
1
School of Electronic Information, Central South University, 410083, Changsha, China
2
School of Physics, Central South University, 410083, Changsha, China
3
School of Automation and Electronic Information, Xiangtan University, 411105, Xiangtan, China
Received:
26
November
2023
Accepted:
18
January
2024
Published online:
12
February
2024
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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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.