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Synchronization and circuit design of a chaotic system with coexisting hidden attractors

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Abstract

This paper investigates an unusual example of a three- dimensional dissipative chaotic flow with quadratic nonlinearites in which there is no equilibrium. This system belongs to a newly introduced category of chaotic systems: systems with hidden attractors which have important and potentially problematic engineering consequences. It is more interesting when we show there are coexisting hidden attractors for some range of parameters. We investigate this system through some analysis, circuit design and finally we use it as a benchmark for synchronization using a Robust Adaptive Sliding Mode Control (RASMC). This synchronization is performed through a nonlinear controller based on Lyapunov Stability Theory to stabilize the error dynamics.

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Authors and Affiliations

  1. College of Applied Sciences Nizwa, Ministry of Higher Education, Nizwa, Sultanate of Oman

    M. Shahzad

  2. School of Electronics and Telecommunications, Hanoi University of Science and Technology, 01 Dai Co Viet, Hanoi, Vietnam

    V.-T. Pham

  3. Physics Department, Faculty of Science, University of Tabuk, PO Box 741, 71491, Tabuk, Saudi Arabia

    M. A. Ahmad

  4. Biomedical Engineering Department, Amirkabir University of Technology, Tehran, 15875-4413, Iran

    S. Jafari & F. Hadaeghi

Authors
  1. M. Shahzad
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  2. V.-T. Pham
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  3. M. A. Ahmad
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  4. S. Jafari
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  5. F. Hadaeghi
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Corresponding author

Correspondence to S. Jafari.

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Shahzad, M., Pham, VT., Ahmad, M.A. et al. Synchronization and circuit design of a chaotic system with coexisting hidden attractors. Eur. Phys. J. Spec. Top. 224, 1637–1652 (2015). https://doi.org/10.1140/epjst/e2015-02485-8

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  • DOI: https://doi.org/10.1140/epjst/e2015-02485-8

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