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Dynamics, synchronization and circuit implementation of a simple fractional-order chaotic system with hidden attractors

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  • Wang, Mengjiao
  • Liao, Xiaohan
  • Deng, Yong
  • Li, Zhijun
  • Su, Yongxin
  • Zeng, Yicheng

Abstract

A simple 4-D fractional-order chaotic system with hidden attractors is studied in this paper. Such a simple system can display distinguished dynamical behaviors. Specially, two different types of multistability are displayed, one of which is caused by changing the initial values of state variables, and the another is caused by introducing a scalar about offset boosting and changing the value of this scalar under the invariant initial conditions. With the view of practical application, the spectral entropy (SE) algorithm is chosen to estimate the complexity of fractional-order chaotic system. In addition, the synchronization of two fractional-order chaotic systems is discussed. Different from the previous numerical simulation scheme, an analog electronic circuit is designed to verify the effectiveness and practicability of the synchronization method. And the hidden hyperchaotic attractors of drive system are successfully captured on the oscilloscope by hardware electronic circuit.

Suggested Citation

  • Wang, Mengjiao & Liao, Xiaohan & Deng, Yong & Li, Zhijun & Su, Yongxin & Zeng, Yicheng, 2020. "Dynamics, synchronization and circuit implementation of a simple fractional-order chaotic system with hidden attractors," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    • Handle: RePEc:eee:chsofr:v:130:y:2020:i:c:s0960077919303418
    DOI: 10.1016/j.chaos.2019.109406
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    References listed on IDEAS

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    Cited by:

    1. Zizhao Xie & Jingru Sun & Yiping Tang & Xin Tang & Oluyomi Simpson & Yichuang Sun, 2023. "A K-SVD Based Compressive Sensing Method for Visual Chaotic Image Encryption," Mathematics, MDPI, vol. 11(7), pages 1-20, March.
    2. Kamal, F.M. & Elsonbaty, A. & Elsaid, A., 2021. "A novel fractional nonautonomous chaotic circuit model and its application to image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    3. Cui, Huizi & Zhou, Lingge & Li, Yan & Kang, Bingyi, 2022. "Belief entropy-of-entropy and its application in the cardiac interbeat interval time series analysis," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    4. Liu, Tianming & Yan, Huizhen & Banerjee, Santo & Mou, Jun, 2021. "A fractional-order chaotic system with hidden attractor and self-excited attractor and its DSP implementation," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    5. Gu, Shuangquan & He, Shaobo & Wang, Huihai & Du, Baoxiang, 2021. "Analysis of three types of initial offset-boosting behavior for a new fractional-order dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    6. Abed-Elhameed, Tarek M. & Mahmoud, Gamal M. & Elbadry, Motaz M. & Ahmed, Mansour E., 2023. "Nonlinear distributed-order models: Adaptive synchronization, image encryption and circuit implementation," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

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