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Analysis and control of multiple chaotic attractors from a three-dimensional system

Author

Listed:
  • Zhong, Xiaoyun
  • Peng, Minfang
  • Tse, Chi K.
  • Guo, Shangjiang
  • Shahidehpour, Mohammad

Abstract

This paper studies a three-dimensional multiple chaotic system with three quadratic nonlinear terms. The system is shown to exhibit multiple periodic attractors and multiple chaotic attractors including a four-scroll chaotic attractor. It is shown analytically and numerically that any neighborhood of the four-scroll chaotic attractor contains repelling sets with positive Lebesgue measures. Moreover, in terms of incommensurate fractional order systems, a simple fractional differentiator-based controller is designed to suppress chaos. Some basic dynamical behaviors of the system are investigated through analytical techniques and numerical simulation.

Suggested Citation

  • Zhong, Xiaoyun & Peng, Minfang & Tse, Chi K. & Guo, Shangjiang & Shahidehpour, Mohammad, 2015. "Analysis and control of multiple chaotic attractors from a three-dimensional system," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 138-150.
    • Handle: RePEc:eee:apmaco:v:268:y:2015:i:c:p:138-150
    DOI: 10.1016/j.amc.2015.06.057
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    References listed on IDEAS

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    1. Aguirre-Hernández, B. & Campos-Cantón, E. & López-Renteria, J.A. & Díaz González, E.C., 2015. "A polynomial approach for generating a monoparametric family of chaotic attractors via switched linear systems," Chaos, Solitons & Fractals, Elsevier, vol. 71(C), pages 100-106.
    2. Liu, Zengrong & Li, Ying & Chen, Guanrong, 2007. "The basin of attraction of the Chen attractor," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1696-1703.
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    Cited by:

    1. Njitacke, Z.T. & kengne, J. & Fotsin, H.B. & Negou, A. Nguomkam & Tchiotsop, D., 2016. "Coexistence of multiple attractors and crisis route to chaos in a novel memristive diode bidge-based Jerk circuit," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 180-197.

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