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Hidden Extreme Multistability in a Novel No-Equilibrium Fractional-Order Chaotic System and Its Synchronization Control

  • General and Applied Physics
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Abstract

Chaotic systems with hidden attractors have received widespread attention recently. In this paper, we construct a new four-dimensional fractional-order chaotic system by adding a further variable in a 3D chaotic system. This newly presented system has no equilibrium points, which reveals that the attractors produced by this system are all hidden. The intricate hidden dynamic properties are investigated by adopting nonlinear dynamical analysis tools such as phase diagrams, bifurcation diagrams, Lyapunov exponents, and chaos diagrams. In particular, the coexisting hidden attractors and extreme multistability are also observed in the system. Furthermore, the electronic circuit of this chaotic system is designed and the corresponding hardware circuit experiment is also achieved. Finally, based on the theory of fractional finite time stability theorem, a suitable finite time synchronization controller is designed. Numerical simulations are provided to verify the effectiveness of the proposed synchronization scheme.

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Acknowledgments

The authors would like to thank the reviewers and the editor for their helpful comments on the manuscript of this paper.

Funding

The authors received funding from the National Natural Science Foundation of China (Grant Nos. 61176032 and 61471310) and the Natural Science Foundation of Hunan Province (Grant Nos.2015JJ2142).

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  1. College of Information Engineering, Xiangtan University, Xiangtan, 411105, Hunan, China

    Siyuan Fang, Zhijun Li, Xu Zhang & Ying Li

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  1. Siyuan Fang
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  2. Zhijun Li
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Correspondence to Zhijun Li.

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Fang, S., Li, Z., Zhang, X. et al. Hidden Extreme Multistability in a Novel No-Equilibrium Fractional-Order Chaotic System and Its Synchronization Control. Braz J Phys 49, 846–858 (2019). https://doi.org/10.1007/s13538-019-00705-1

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