Although memristor has been widely discussed in recent years, the topic of memristor in discrete domain is rarely mentioned. This paper presents a higher dimensional chaotic map based on the discrete memristor, and the dynamic behavior of memristor at different positions is investigated by chaotic attractor phase diagram, bifurcation diagram, system state analysis and complexity algorithm. Numerical simulations show that the discrete memristor model can not only enlarge the hyperchaotic region of the original system, but also enhance the system complexity. Furthermore, the change of memristor position in the system leads to different performance. These deserve further study and lay the foundation for the future applications of the discrete memristor.

尽管近年来对忆阻器进行了广泛讨论，但很少提及离散域中的忆阻器主题。本文提出了一种基于离散忆阻器的高维混沌图，并通过混沌吸引子相图，分叉图，系统状态分析和复杂度算法研究了忆阻器在不同位置的动态行为。数值模拟表明，离散忆阻器模型不仅可以扩大原始系统的超混沌区域，而且可以提高系统的复杂度。此外，忆阻器位置在系统中的变化会导致不同的性能。这些值得进一步研究，并为分立忆阻器的未来应用奠定基础。