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Hidden dynamics, synchronization, and circuit implementation of a fractional-order memristor-based chaotic system

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Abstract

Fractional calculus has always been regarded as an ideal mathematical tool to describe the memory of complex systems and special materials. A fractional-order memristor-based chaotic system with hidden dynamics is studied in this paper. The system can exhibit excellent dynamic behavior by introducing a quadratic nonlinear memristor. Asymmetric coexistence occurs when both the order and parameter change. Considering the practical application of fractional-order system, the spectral entropy (SE) algorithm is used to investigate the complexity of the system. Besides, synchronous experiment between two fractional-order system is carried out and the synchronization circuit is also designed. To verify the numerical simulation results, the hardware circuit is constructed, and the hidden attractors are successfully captured on the oscilloscope by hardware electronic circuit.

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Acknowledgements

This work was supported by Research Foundation of Education Department of Hunan Province, China (Grant No. 20B567); the Natural Science Foundation of Hunan Province, China (Grant No. 2019JJ50624); and the National Natural Science Foundation of China (Grant No. 62071411).

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Authors and Affiliations

  1. School of Automation and Electronic Information, Xiangtan, China

    Mengjiao Wang, Bingqing Deng, Min Deng & Yibing Zhang

  2. School of Computer Science and School of Cyberspace Science, Xiangtan, China

    Yuexi Peng

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  1. Mengjiao Wang
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  2. Bingqing Deng
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  4. Min Deng
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Correspondence to Mengjiao Wang.

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Wang, M., Deng, B., Peng, Y. et al. Hidden dynamics, synchronization, and circuit implementation of a fractional-order memristor-based chaotic system. Eur. Phys. J. Spec. Top. 231, 3171–3185 (2022). https://doi.org/10.1140/epjs/s11734-022-00568-9

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