Discrete memristor (DM) has been extensively used to enhance the complexity of simple chaotic maps due to its special nonlinearity. Yet, the chaotic properties inherent to DM have not been thoroughly explored. This article introduces a simple oscillatory term to the DM model and constructs four hyperchaotic maps. In these maps, the coupling of the ideal DM with the oscillatory term results in maps without fixed points, generating hidden hyperchaotic attractors. The introduction of the oscillatory term into DMs exhibits diverse dynamical behaviors, including coexisting bistable attractors, infinitely many homogeneously coexisting attractors, heterogeneously coexisting attractors, and symmetrically coexisting attractors. The performances of the sequences generated by these maps are evaluated, and they are successfully applied to the design of pseudorandom number generators (PRNGs). The research results demonstrate that the outputs of all four maps, as well as the pseudorandom numbers generated by the PRNG, exhibit high randomness. Finally, a hardware platform is constructed to successfully implement these maps.

中文翻译：

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具有不同动力学的二维离散忆阻振荡超混沌映射


离散忆阻器（DM）由于其特殊的非线性而被广泛用于增强简单混沌映射的复杂性。然而，DM 固有的混沌特性尚未得到彻底探索。本文向 DM 模型引入了一个简单的振荡项，并构造了四个超混沌映射。在这些图中，理想 DM 与振荡项的耦合导致图中没有固定点，从而生成隐藏的超混沌吸引子。将振荡项引入DM中表现出多种动力学行为，包括共存双稳态吸引子、无限多个同质共存吸引子、异质共存吸引子和对称共存吸引子。对这些映射生成的序列的性能进行了评估，并将它们成功应用于伪随机数生成器（PRNG）的设计。研究结果表明，所有四个映射的输出以及 PRNG 生成的伪随机数都表现出很高的随机性。最后，构建了一个硬件平台来成功实现这些地图。