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Control, electronic circuit application and fractional-order analysis of hidden chaotic attractors in the self-exciting homopolar disc dynamo

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  • Wei, Zhouchao
  • Akgul, Akif
  • Kocamaz, Uğur Erkin
  • Moroz, Irene
  • Zhang, Wei

Abstract

Based on the segmented disc dynamo proposed by H. K. Moffatt, we give out the hidden chaotic attractors, which can show the imperfection in the dynamo model. In this paper. control of hidden chaos in the model is investigated by Lyapunov based nonlinear feedback controllers, sliding mode controllers and hybrid combination of them. Numerical simulations on the comparative analyses are presented. Moreover, with the aid of ORCAD-Pspice and oscilloscope, hidden chaos can be implemented by electronic circuit. Compared with the phase portraits using MATLAB, the simulation results of the oscilloscope outputs verify the effectiveness of electronic circuit design. Finally, in order to consider the effects of fractional order, we analyze the fractional order chaotic system (FOCS) and consider its FPGA implementation for the self-exciting homopolar disc dynamo. The results are helpful for us to better understand the dynamics behavior of disc dynamos.

Suggested Citation

  • Wei, Zhouchao & Akgul, Akif & Kocamaz, Uğur Erkin & Moroz, Irene & Zhang, Wei, 2018. "Control, electronic circuit application and fractional-order analysis of hidden chaotic attractors in the self-exciting homopolar disc dynamo," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 157-168.
    • Handle: RePEc:eee:chsofr:v:111:y:2018:i:c:p:157-168
    DOI: 10.1016/j.chaos.2018.04.020
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    References listed on IDEAS

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    1. Park, Ju H., 2005. "Chaos synchronization of a chaotic system via nonlinear control," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 579-584.
    2. Chen, Hsien-Keng, 2005. "Global chaos synchronization of new chaotic systems via nonlinear control," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1245-1251.
    3. Chang, Jen-Fuh & Hung, Meei-Ling & Yang, Yi-Sung & Liao, Teh-Lu & Yan, Jun-Juh, 2008. "Controlling chaos of the family of Rössler systems using sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 609-622.
    4. Peng, Chao-Chung & Chen, Chieh-Li, 2008. "Robust chaotic control of Lorenz system by backstepping design," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 598-608.
    5. Karthikeyan Rajagopal & Anitha Karthikeyan & Prakash Duraisamy, 2017. "Hyperchaotic Chameleon: Fractional Order FPGA Implementation," Complexity, Hindawi, vol. 2017, pages 1-16, May.
    6. Jin-Qing Fang & Yiguang Hong & Huashu Qin & Guanrong Chen, 2000. "Nonlinear control of chaotic systems:A switching manifold approach," Discrete Dynamics in Nature and Society, Hindawi, vol. 4, pages 1-11, January.
    7. Yassen, M.T., 2005. "Controlling chaos and synchronization for new chaotic system using linear feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 913-920.
    8. Karthikeyan Rajagopal & Laarem Guessas & Anitha Karthikeyan & Ashokkumar Srinivasan & Girma Adam, 2017. "Fractional Order Memristor No Equilibrium Chaotic System with Its Adaptive Sliding Mode Synchronization and Genetically Optimized Fractional Order PID Synchronization," Complexity, Hindawi, vol. 2017, pages 1-19, March.
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    Cited by:

    1. Dutta, Maitreyee & Roy, Binoy Krishna, 2021. "A new memductance-based fractional-order chaotic system and its fixed-time synchronisation," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    2. Deng, Shuning & Ji, Jinchen & Wen, Guilin & Xu, Huidong, 2021. "A comparative study of the dynamics of a three-disk dynamo system with and without time delay," Applied Mathematics and Computation, Elsevier, vol. 399(C).
    3. Nian, Fuzhong & Liu, Xinmeng & Zhang, Yaqiong, 2018. "Sliding mode synchronization of fractional-order complex chaotic system with parametric and external disturbances," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 22-28.

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