The realization of real memristor makes it be a very popular topic in recent years. However, the topic about discrete memristor model is rarely discussed. In this paper, a discrete memristor model is proposed based on the difference theory, and the three fingerprints characteristics are proved for this model according to the definition of the generalized memristor. This discrete model is applied to Hénon map, and we designed a new chaotic map called the discrete memristor-based Hénon map. Its dynamical behaviors are analyzed by attractor phase diagram, bifurcation diagram, Lyapunov exponent spectrum, and spectral entropy complexity algorithm. Simulation results show the performance of Hénon map is improved by applying the discrete memristor.

真正的忆阻器的实现使其成为近年来非常受欢迎的话题。但是，关于离散忆阻器模型的话题很少讨论。本文基于差分理论，提出了一种离散忆阻器模型，并根据广义忆阻器的定义证明了该模型的三个指纹特征。这个离散模型被应用于Hénon映射，并且我们设计了一个新的混沌映射，称为基于离散忆阻器的Hénon映射。通过吸引子相图，分叉图，李雅普诺夫指数谱和谱熵复杂度算法分析了其动力学行为。仿真结果表明，通过应用离散忆阻器可以改善Hénon映射的性能。