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Tri-valued memristor-based hyper-chaotic system with hidden and coexistent attractors

Author

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  • Wang, Xiaoyuan
  • Gao, Meng
  • Iu, Herbert Ho-Ching
  • Wang, Chunhua

Abstract

Recently, the nonlinear dynamics of memristor has attracted much attention. In this paper, a novel four-dimensional hyper-chaotic system (4D-HCS) based on a tri-valued memristor is found. Theoretical analysis shows that the 4D-HCS has complex hyper-chaotic dynamics such as hidden attractors and coexistent attractors. We also experimentally analyze the dynamics behaviors of the 4D-HCS in aspects of the phase diagram, bifurcation diagram, Lyapunov exponential spectrum, power spectrum and the correlation coefficient. To rigorously verify the chaotic behavior, we analyze the topological horseshoe of the system and calculate the topological entropy. In addition, the comparison with binary-valued memristor-based chaotic system shows that a chaotic system with a tri-valued memristor can generate hyper-chaos and coexistent attractors, while the one with a binary-valued memristor cannot. This finding suggests that applying three- or multi-value memristors in chaotic circuits can produce more complex dynamic properties than binary-valued memristors. To show the easy implementation of the 4D-HCS, we implement the 4D-HCS in an analogue circuit-based hardware platform, and the implementation results are consistent with the theoretical analysis. Finally, using the 4D-HCS, we design a pseudorandom number generator to explore its potential application in cryptography.

Suggested Citation

  • Wang, Xiaoyuan & Gao, Meng & Iu, Herbert Ho-Ching & Wang, Chunhua, 2022. "Tri-valued memristor-based hyper-chaotic system with hidden and coexistent attractors," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    • Handle: RePEc:eee:chsofr:v:159:y:2022:i:c:s0960077922003873
    DOI: 10.1016/j.chaos.2022.112177
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    References listed on IDEAS

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    1. Xiaoyuan Wang & Xue Zhang & Meng Gao, 2020. "A Novel Voltage-Controlled Tri-Valued Memristor and Its Application in Chaotic System," Complexity, Hindawi, vol. 2020, pages 1-8, July.
    2. Fei Yu & Li Liu & Hui Shen & Zinan Zhang & Yuanyuan Huang & Shuo Cai & Zelin Deng & Qiuzhen Wan, 2020. "Multistability Analysis, Coexisting Multiple Attractors, and FPGA Implementation of Yu–Wang Four-Wing Chaotic System," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-16, August.
    3. Xiaoyuan Wang & Xiaotao Min & Pengfei Zhou & Dongsheng Yu, 2020. "Hyperchaotic Circuit Based on Memristor Feedback with Multistability and Symmetries," Complexity, Hindawi, vol. 2020, pages 1-10, February.
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    Citations

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    Cited by:

    1. Xiaoyuan Wang & Xinrui Zhang & Meng Gao & Yuanze Tian & Chunhua Wang & Herbert Ho-Ching Iu, 2023. "A Color Image Encryption Algorithm Based on Hash Table, Hilbert Curve and Hyper-Chaotic Synchronization," Mathematics, MDPI, vol. 11(3), pages 1-18, January.
    2. Wang, Ning & Cui, Mengkai & Yu, Xihong & Shan, Yufan & Xu, Quan, 2023. "Generating multi-folded hidden Chua’s attractors: Two-case study," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    3. 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).
    4. Wang, Ning & Xu, Dan & Li, Ze & Xu, Quan, 2023. "A general configuration for nonlinear circuit employing current-controlled nonlinearity: Application in Chua’s circuit," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    5. Wang, Zhen & Ahmadi, Atefeh & Tian, Huaigu & Jafari, Sajad & Chen, Guanrong, 2023. "Lower-dimensional simple chaotic systems with spectacular features," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).

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