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Complex dynamics and encryption application of a 3D dual-memristor oscillatory hyperchaotic map

Author

Listed:
  • Lai, Qiang
  • Zhu, Chongkun
  • Qin, Minghong
  • Wan, Zhiqiang

Abstract

Unlike high-dimensional hyperchaotic maps constructed using continuous memristors (CMs), discrete memristors (DMs) are widely favored by researchers because of their unique advantages. In view of this, a novel memristive hyperchaotic map by applying a sinusoidal transformation to one DM and paralleling it with another, while introducing the simple oscillatory term has been proposed. This map exhibits significant structural characteristics, particularly without fixed points. Numerical simulations reveal the dynamical behaviors that dependent on control parameters and the presence of infinite hidden coexisting attractors related to initial values. Furthermore, the map has been successfully applied in the design of a pseudorandom number generator (PRNG). A microcontroller-based digital hardware platform has also been developed to implement this map. Lastly, the application of the map in image encryption provides valuable insights into the use of discrete memristive maps in chaos engineering.

Suggested Citation

  • Lai, Qiang & Zhu, Chongkun & Qin, Minghong & Wan, Zhiqiang, 2025. "Complex dynamics and encryption application of a 3D dual-memristor oscillatory hyperchaotic map," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 236(C), pages 270-283.
    • Handle: RePEc:eee:matcom:v:236:y:2025:i:c:p:270-283
    DOI: 10.1016/j.matcom.2025.04.005
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    References listed on IDEAS

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    1. Lai, Qiang & Yang, Liang, 2023. "Discrete memristor applied to construct neural networks with homogeneous and heterogeneous coexisting attractors," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    2. Yuan, Fang & Xing, Guibin & Deng, Yue, 2023. "Flexible cascade and parallel operations of discrete memristor," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    3. Wan, Qiuzhen & Li, Fei & Chen, Simiao & Yang, Qiao, 2023. "Symmetric multi-scroll attractors in magnetized Hopfield neural network under pulse controlled memristor and pulse current stimulation," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    4. Liu, Xinkang & Sun, Kehui & Wang, Huihai & He, Shaobo, 2023. "A class of novel discrete memristive chaotic map," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    5. Bao, H. & Gu, Y. & Xu, Q. & Zhang, X. & Bao, B., 2022. "Parallel bi-memristor hyperchaotic map with extreme multistability," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    6. Fan, Zhenyi & Zhang, Chenkai & Wang, Yiming & Du, Baoxiang, 2023. "Construction, dynamic analysis and DSP implementation of a novel 3D discrete memristive hyperchaotic map," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    7. Lai, Qiang & Chen, Zhijie, 2023. "Dynamical analysis and finite-time synchronization of grid-scroll memristive chaotic system without equilibrium," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
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