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Design and realization of discrete memristive hyperchaotic map with application in image encryption

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  • Lai, Qiang
  • Yang, Liang
  • Liu, Yuan

Abstract

The investigation of discrete memristive chaotic systems with complex dynamics has been an interesting and meaningful research work. This paper is devoted to constructing a hyperchaotic system with no fixed point and infinitely many coexisting attractors. The memristive Gaussian map (MGM) is coupled by a sinusoidal discrete memristor with the Gaussian map and induces extreme multistability associated with the initial state due to the import of sinusoidal nonlinearity. Creatively, the iterative number is imported into the system as a variable, which effectively boosts the complexity of its export. The most remarkable feature of the system is a large range of chaos and hyperchaos captured under multiple sets of parameters, and with various coexisting attractors. In addition, digital experiments are designed to verify the feasibility of the hardware implementation, an image encryption algorithm and PRNG are proposed based on the MGM chaotic sequence.

Suggested Citation

  • Lai, Qiang & Yang, Liang & Liu, Yuan, 2022. "Design and realization of discrete memristive hyperchaotic map with application in image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    • Handle: RePEc:eee:chsofr:v:165:y:2022:i:p1:s0960077922009602
    DOI: 10.1016/j.chaos.2022.112781
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    1. Lai, Qiang & Hua, Hanqiang & Zhao, Xiao-Wen & Erkan, Uǧur & Toktas, Abdurrahim, 2023. "Image encryption using fission diffusion process and a new hyperchaotic map," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
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    5. 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).
    6. Balaraman, Sundarambal & Kengne, Jacques & Kamga Fogue, M.S. & Rajagopal, Karthikeyan, 2023. "From coexisting attractors to multi-spiral chaos in a ring of three coupled excitation-free Duffing oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    7. Li, Yongxin & Li, Chunbiao & Zhong, Qing & Zhao, Yibo & Yang, Yong, 2024. "Coexisting hollow chaotic attractors within a steep parameter interval," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    8. Jia, Junen & Wang, Chunni & Zhang, Xiaofeng & Zhu, Zhigang, 2024. "Energy and self-adaption in a memristive map neuron," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    9. Wu, Huagan & Gu, Jinxiang & Guo, Yixuan & Chen, Mo & Xu, Quan, 2024. "Biphasic action potentials in an individual cellular neural network cell," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    10. 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).
    11. Lu, Yang & Gong, Mengxin & Gan, Zhihua & Chai, Xiuli & Cao, Lvchen & Wang, Binjie, 2023. "Exploiting one-dimensional improved Chebyshev chaotic system and partitioned diffusion based on the divide-and-conquer principle for 3D medical model encryption," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    12. SaberiKamarposhti, Morteza & Ghorbani, Amirabbas & Yadollahi, Mehdi, 2024. "A comprehensive survey on image encryption: Taxonomy, challenges, and future directions," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    13. Hairong Lin & Chunhua Wang & Fei Yu & Jingru Sun & Sichun Du & Zekun Deng & Quanli Deng, 2023. "A Review of Chaotic Systems Based on Memristive Hopfield Neural Networks," Mathematics, MDPI, vol. 11(6), pages 1-18, March.
    14. Lai, Qiang & Hu, Genwen & Erkan, Uǧur & Toktas, Abdurrahim, 2023. "High-efficiency medical image encryption method based on 2D Logistic-Gaussian hyperchaotic map," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    15. Fei Yu & Wuxiong Zhang & Xiaoli Xiao & Wei Yao & Shuo Cai & Jin Zhang & Chunhua Wang & Yi Li, 2023. "Dynamic Analysis and FPGA Implementation of a New, Simple 5D Memristive Hyperchaotic Sprott-C System," Mathematics, MDPI, vol. 11(3), pages 1-15, January.

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