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Synchronization and Electronic Circuit Application of Hidden Hyperchaos in a Four-Dimensional Self-Exciting Homopolar Disc Dynamo without Equilibria

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  • Yu Feng
  • Zhouchao Wei
  • Uğur Erkin Kocamaz
  • Akif Akgül
  • Irene Moroz

Abstract

We introduce and investigate a four-dimensional hidden hyperchaotic system without equilibria, which is obtained by augmenting the three-dimensional self-exciting homopolar disc dynamo due to Moffatt with an additional control variable. Synchronization of two such coupled disc dynamo models is investigated by active control and sliding mode control methods. Numerical integrations show that sliding mode control provides a better synchronization in time but causes chattering. The solution is obtained by switching to active control when the synchronization errors become very small. In addition, the electronic circuit of the four-dimensional hyperchaotic system has been realized in ORCAD-PSpice and on the oscilloscope by amplitude values, verifying the results from the numerical experiments.

Suggested Citation

  • Yu Feng & Zhouchao Wei & Uğur Erkin Kocamaz & Akif Akgül & Irene Moroz, 2017. "Synchronization and Electronic Circuit Application of Hidden Hyperchaos in a Four-Dimensional Self-Exciting Homopolar Disc Dynamo without Equilibria," Complexity, Hindawi, vol. 2017, pages 1-11, May.
    • Handle: RePEc:hin:complx:7101927
    DOI: 10.1155/2017/7101927
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    References listed on IDEAS

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    2. Almeida, David I. Rosas & Alvarez, Joaquín & Barajas, Juan Gonzalo, 2006. "Robust synchronization of Sprott circuits using sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 11-18.
    3. El-Dessoky, M.M., 2009. "Synchronization and anti-synchronization of a hyperchaotic Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1790-1797.
    4. Chen, Aimin & Lu, Junan & Lü, Jinhu & Yu, Simin, 2006. "Generating hyperchaotic Lü attractor via state feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 103-110.
    5. Uçar, Ahmet & Lonngren, Karl E. & Bai, Er-Wei, 2006. "Synchronization of the unified chaotic systems via active control," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1292-1297.
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    Cited by:

    1. Abir Lassoued & Olfa Boubaker, 2017. "Dynamic Analysis and Circuit Design of a Novel Hyperchaotic System with Fractional-Order Terms," Complexity, Hindawi, vol. 2017, pages 1-10, October.
    2. Ping Zhou & Meihua Ke, 2017. "A New 3D Autonomous Continuous System with Two Isolated Chaotic Attractors and Its Topological Horseshoes," Complexity, Hindawi, vol. 2017, pages 1-7, November.

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