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Bifurcation Analysis and Sliding Mode Control of Chaotic Vibrations in an Autonomous System

Author

Listed:
  • Wenju Du
  • Yandong Chu
  • Jiangang Zhang
  • Yingxiang Chang
  • Jianning Yu
  • Xinlei An

Abstract

We study the bifurcations and sliding mode control of chaotic vibrations in an autonomous system. More precisely, a Hopf bifurcation controller is designed so as to control the unstable subcritical Hopf bifurcation to the stable supercritical Hopf bifurcation. Research result shows that the control method can work very well in Hopf bifurcation control. Besides, we controlled the system to any fixed point and any periodic orbit to eliminate the chaotic vibration by means of sliding mode method. And the numerical simulations were presented to confirm the effectiveness of the controller.

Suggested Citation

  • Wenju Du & Yandong Chu & Jiangang Zhang & Yingxiang Chang & Jianning Yu & Xinlei An, 2014. "Bifurcation Analysis and Sliding Mode Control of Chaotic Vibrations in an Autonomous System," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:726491
    DOI: 10.1155/2014/726491
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    References listed on IDEAS

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    1. Mello, L.F. & Messias, M. & Braga, D.C., 2008. "Bifurcation analysis of a new Lorenz-like chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1244-1255.
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    Cited by:

    1. Zhiqiang Cheng & Wencheng Wang & Yuezhang Dai & Lun Li, 2022. "A High‐Security Privacy Image Encryption Algorithm Based on Chaos and Double Encryption Strategy," Journal of Applied Mathematics, John Wiley & Sons, vol. 2022(1).

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