This paper presents a chaotic system with hidden attractors by introducing a tri-valued memristor into the Liu chaotic system. The attractors have a rich topology, as shown by the analysis of the phase diagram, Poincaré diagram, Lyapunov exponential spectrum and bifurcation diagram, and we try to summarize the regularity of the system characteristics within a certain range of controllable parameters. We analyzed attractors with strange shapes by setting different parameters, and the multistability and the transient behavior is analyzed, which reflects the high complexity of the system, The complexity characteristics of the system are also analyzed by calculating the SE value and C0 complexity, the corresponding circuit is designed, and the simulation analysis of the system is carried out to verify the physical realizability of the system. Finally, this system is applied to image encryption to analyze its security from a histogram and correlation perspective. These findings provide a reference value for the tri-valued memristor based system for encryption applications.

Graphical abstract

中文翻译：

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具有隐藏吸引子的三值忆阻混沌系统及其图像加密应用

本文通过在刘氏混沌系统中引入三值忆阻器，提出了一种具有隐藏吸引子的混沌系统。通过对相图、庞加莱图、李亚普诺夫指数谱和分岔图的分析表明，吸引子具有丰富的拓扑结构，并试图总结系统特性在一定可控参数范围内的规律性。我们通过设置不同的参数来分析形状奇异的吸引子，并分析其多稳定性和瞬态行为，这体现了系统的高复杂性，还通过计算SE值和C0复杂度来分析系统的复杂性特征，相应的设计了电路,并对系统进行了仿真分析,验证了系统的物理实现性。最后将该系统应用于图像加密，从直方图和相关性角度分析其安全性。这些研究结果为基于三值忆阻器的加密应用系统提供了参考价值。

图形概要