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A Wide-Range Adjustable Conservative Memristive Hyperchaotic System with Transient Quasi-Periodic Characteristics and Encryption Application

Author

Listed:
  • Fei Yu

    (School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha 410114, China)

  • Bohong Tan

    (School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha 410114, China)

  • Ting He

    (School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha 410114, China)

  • Shaoqi He

    (School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha 410114, China)

  • Yuanyuan Huang

    (School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha 410114, China)

  • Shuo Cai

    (School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha 410114, China)

  • Hairong Lin

    (School of Electronic Information, Central South University, Changsha 410083, China)

Abstract

In comparison with dissipative chaos, conservative chaos is better equipped to handle the risks associated with the reconstruction of phase space due to the absence of attractors. This paper proposes a novel five-dimensional (5D) conservative memristive hyperchaotic system (CMHS), by incorporating memristors into a four-dimensional (4D) conservative chaotic system (CCS). We conducted a comprehensive analysis, using Lyapunov exponent diagrams, bifurcation diagrams, phase portraits, equilibrium points, and spectral entropy maps to thoroughly verify the system’s chaotic and conservative properties. The system exhibited characteristics such as hyperchaos and multi-stability over an ultra-wide range of parameters and initial values, accompanied by transient quasi-periodic phenomena. Subsequently, the pseudorandom sequences generated by the new system were tested and demonstrated excellent performance, passing all the tests set by the National Institute of Standards and Technology (NIST). In the final stage of the research, an image-encryption application based on the 5D CMHS was proposed. Through security analysis, the feasibility and security of the image-encryption algorithm were confirmed.

Suggested Citation

  • Fei Yu & Bohong Tan & Ting He & Shaoqi He & Yuanyuan Huang & Shuo Cai & Hairong Lin, 2025. "A Wide-Range Adjustable Conservative Memristive Hyperchaotic System with Transient Quasi-Periodic Characteristics and Encryption Application," Mathematics, MDPI, vol. 13(5), pages 1-23, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:5:p:726-:d:1598290
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    References listed on IDEAS

    as
    1. Shenli Zhu & Xiaoheng Deng & Wendong Zhang & Congxu Zhu, 2023. "Construction of a New 2D Hyperchaotic Map with Application in Efficient Pseudo-Random Number Generator Design and Color Image Encryption," Mathematics, MDPI, vol. 11(14), pages 1-23, July.
    2. Wang, Chunhua & Luo, Dingwei & Deng, Quanli & Yang, Gang, 2024. "Dynamics analysis and FPGA implementation of discrete memristive cellular neural network with heterogeneous activation functions," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
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    4. Ojoniyi, Olurotimi S. & Njah, Abdulahi N., 2016. "A 5D hyperchaotic Sprott B system with coexisting hidden attractors," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 172-181.
    5. Zhou, Shuang & Qiu, Yuyu & Qi, Guoyuan & Zhang, Yingqian, 2023. "A new conservative chaotic system and its application in image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    6. Fei Yu & Shuai Xu & Yue Lin & Ting He & Chaoran Wu & Hairong Lin, 2024. "Design and Analysis of a Novel Fractional-Order System with Hidden Dynamics, Hyperchaotic Behavior and Multi-Scroll Attractors," Mathematics, MDPI, vol. 12(14), pages 1-22, July.
    7. Jia, Hongyan & Shi, Wenxin & Wang, Lei & Qi, Guoyuan, 2020. "Energy analysis of Sprott-A system and generation of a new Hamiltonian conservative chaotic system with coexisting hidden attractors," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
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