Construction, dynamic analysis and DSP implementation of a novel 3D discrete memristive hyperchaotic map

In this paper, a three-dimensional discrete memristive hyperchaotic map (3DMCHM) with a complex structure and rich, dynamic characteristics is designed by using a discrete charge-controlled memristor. By introducing the offset control, amplitude control, and coupling parameters, we have found that changing the parameters and initial values can lead to different outcomes. We have discovered that modifying the parameters and initial values yields significant results. The 3DMCHM exhibits several dynamic characteristics, including complex offset behavior, multi-vortex-like behavior, separate structure phenomenon, transient-like phenomenon, expansion and contraction phenomenon, and inversion symmetry phenomenon. The offset behavior appears with multi-state transition controlled by parameters. Additionally, we have discovered that by changing the related parameters, The 3DMCHM can evolve from period, period doubling, chaos, and hyperchaos. We have conducted tests to assess the complexity and randomness of the 3DMCHM and have verified its high complexity and good randomness. Finally, we have successfully implemented the 3DMCHM using the DSP hardware circuit, thereby confirming the feasibility and potential applications of the 3DMCHM.