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A tri-valued memristive chaotic system with hidden attractors and its image encryption application

  • Regular Article - Statistical and Nonlinear Physics
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Abstract

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

The left box is descriptions of how to build the system, and the right box is the descriptions of the phenomena produced by the three parameters a,b and h,the middle part is the dynamics analysis, complexity analysis, and circuit design of the system

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Data Availability Statement

The data used in this article are calculated by software Matlab to support our results and analysis, and do not use any open source or closed-source databases.

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Funding

This project was supported by the Guizhou Provincial Basic Research Program (Natural Science) (Grant no. ZK [2022] 042, ZK [2021] 051, ZK [2023] 013), the National Natural Science Foundation of China (Grant No. 52262021, 51661005, and 11964005), the Industry and Education Combination Innovation Platform of Intelligent Manufacturing and Graduate Joint Training Base at Guizhou University (No. 2020–520000-83–01-324061) and the Fostering Project of Guizhou University (Grant No. [2020]33).

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Authors and Affiliations

  1. Gui Zhou University, Guizhou, China

    Wang Yun, Chen Qian, Liang Bo & Hu Chen-yang

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  1. Wang Yun
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  2. Chen Qian
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  3. Liang Bo
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Contributions

Wang Yun: Conceptualization, Methodology, Software, Investigation, Formal Analysis, Writing—Original Draft; Chen Qian: Conceptualization, Funding Acquisition, Resources, Supervision; Liang Bo: Visualization, Writing—Review & Editing; Hu Chen-Yang: Data Curation, Writing—Original Draft.

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Correspondence to Chen Qian.

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Yun, W., Qian, C., Bo, L. et al. A tri-valued memristive chaotic system with hidden attractors and its image encryption application. Eur. Phys. J. B 97, 30 (2024). https://doi.org/10.1140/epjb/s10051-024-00662-y

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