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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.

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  • 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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    Cited by:

    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).
    2. Lai, Qiang & Chen, Zhijie, 2023. "Grid-scroll memristive chaotic system with application to image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    3. 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).
    4. 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).
    5. 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).
    6. 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.
    7. 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.
    8. 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).
    9. 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).
    10. 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).

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