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

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.