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Chin. Phys. B, 2021, Vol. 30(2): 020501    DOI: 10.1088/1674-1056/abbbe4
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Analysis and implementation of new fractional-order multi-scroll hidden attractors

Li Cui(崔力)†, Wen-Hui Luo(雒文辉), and Qing-Li Ou(欧青立)
Hunan University of Science and Technology, Xiangtan 411201, China
Abstract  To improve the complexity of chaotic signals, in this paper we first put forward a new three-dimensional quadratic fractional-order multi-scroll hidden chaotic system, then we use the Adomian decomposition algorithm to solve the proposed fractional-order chaotic system and obtain the chaotic phase diagrams of different orders, as well as the Lyaponov exponent spectrum, bifurcation diagram, and SE complexity of the 0.99-order system. In the process of analyzing the system, we find that the system possesses the dynamic behaviors of hidden attractors and hidden bifurcations. Next, we also propose a method of using the Lyapunov exponents to describe the basins of attraction of the chaotic system in the matlab environment for the first time, and obtain the basins of attraction under different order conditions. Finally, we construct an analog circuit system of the fractional-order chaotic system by using an equivalent circuit module of the fractional-order integral operators, thus realizing the 0.9-order multi-scroll hidden chaotic attractors.
Keywords:  fractional order      hidden attractor      hidden bifurcation      basins of attraction      circuit implementation  
Received:  12 August 2020      Revised:  11 September 2020      Accepted manuscript online:  28 September 2020
PACS:  05.45-a  
  05.45.Ac (Low-dimensional chaos)  
  05.30.Pr (Fractional statistics systems)  
  05.45.Df (Fractals)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 61561022 and 61672226).
Corresponding Authors:  Corresponding author. E-mail: licui@hnust.edu.cn   

Cite this article: 

Li Cui(崔力), Wen-Hui Luo(雒文辉), and Qing-Li Ou(欧青立) Analysis and implementation of new fractional-order multi-scroll hidden attractors 2021 Chin. Phys. B 30 020501

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