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Discrete fracmemristor-based chaotic map by Grunwald–Letnikov difference and its circuit implementation

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  • Peng, Yuexi
  • Liu, Jun
  • He, Shaobo
  • Sun, Kehui

Abstract

The topic of discrete memristor has attracted more and more attention in recent years, but there is not enough discussion about discrete memristor under the fractional-order difference definition, especially for the system model defined by Grunwald–Letnikov. In this paper, a discrete fractional-order memristor model based on Grunwald–Letnikov definition is derived, and two new chaotic maps are designed based on this fractional-order model. Dynamic behaviors are investigated by the volt–ampere curve, bifurcation diagram, Lyapunov exponent spectrum, attractor phase diagram and fuzzy entropy complexity algorithm. Simulation results show that the two fractional-order systems can produce rich dynamic behaviors with the change of fractional order value, and both of them can present hyperchaos. Finally, the proposed systems are implemented in FPGA digital circuit and analog circuit respectively, and the phenomena in the numerical simulation are verified.

Suggested Citation

  • Peng, Yuexi & Liu, Jun & He, Shaobo & Sun, Kehui, 2023. "Discrete fracmemristor-based chaotic map by Grunwald–Letnikov difference and its circuit implementation," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    • Handle: RePEc:eee:chsofr:v:171:y:2023:i:c:s0960077923003302
    DOI: 10.1016/j.chaos.2023.113429
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    References listed on IDEAS

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    1. Peng, Yuexi & Sun, Kehui & Peng, Dong & Ai, Wei, 2019. "Dynamics of a higher dimensional fractional-order chaotic map," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 96-107.
    2. Lai, Qiang & Lai, Cong & Zhang, Hui & Li, Chunbiao, 2022. "Hidden coexisting hyperchaos of new memristive neuron model and its application in image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    3. Min, Fuhong & Zhang, Wen & Ji, Ziyi & Zhang, Lei, 2021. "Switching dynamics of a non-autonomous FitzHugh-Nagumo circuit with piecewise-linear flux-controlled memristor," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    4. Ouannas, Adel & Khennaoui, Amina-Aicha & Odibat, Zaid & Pham, Viet-Thanh & Grassi, Giuseppe, 2019. "On the dynamics, control and synchronization of fractional-order Ikeda map," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 108-115.
    5. Kim, Tae-Hyeon & Kim, Sungjoon & Hong, Kyungho & Park, Jinwoo & Hwang, Yeongjin & Park, Byung-Gook & Kim, Hyungjin, 2021. "Multilevel switching memristor by compliance current adjustment for off-chip training of neuromorphic system," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
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    Cited by:

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    2. Wei, Yiheng & Su, Nan & Zhao, Linlin & Cao, Jinde, 2023. "LMI based stability condition for delta fractional order system with sector approximation," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    3. Tareq Hamadneh & Souad Bensid Ahmed & Hassan Al-Tarawneh & Omar Alsayyed & Gharib Mousa Gharib & Maha S. Al Soudi & Abderrahmane Abbes & Adel Ouannas, 2023. "The New Four-Dimensional Fractional Chaotic Map with Constant and Variable-Order: Chaos, Control and Synchronization," Mathematics, MDPI, vol. 11(20), pages 1-19, October.
    4. Mayada Abualhomos & Abderrahmane Abbes & Gharib Mousa Gharib & Abdallah Shihadeh & Maha S. Al Soudi & Ahmed Atallah Alsaraireh & Adel Ouannas, 2023. "Bifurcation, Hidden Chaos, Entropy and Control in Hénon-Based Fractional Memristor Map with Commensurate and Incommensurate Orders," Mathematics, MDPI, vol. 11(19), pages 1-19, October.
    5. Zhao, Zhigao & Chen, Fei & He, Xianghui & Lan, Pengfei & Chen, Diyi & Yin, Xiuxing & Yang, Jiandong, 2024. "A universal hydraulic-mechanical diagnostic framework based on feature extraction of abnormal on-field measurements: Application in micro pumped storage system," Applied Energy, Elsevier, vol. 357(C).

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