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Control of Hopf Bifurcation in Autonomous System Based on Washout Filter

Author

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

Abstract

In order to further understand a Lorenz‐like system, we study the stability of the equilibrium points and the existence of Hopf bifurcation by center manifold theorem and normal form theory. More precisely, we designed a washout controller such that the equilibrium E0 undergoes a controllable Hopf bifurcation, and by adjusting the controller parameters, we delayed Hopf bifurcation phenomenon of the equilibrium E+. Besides, numerical simulation is given to illustrate the theoretical analysis. Finally, two possible electronic circuits are given to realize the uncontrolled and the controlled systems.

Suggested Citation

  • Wenju Du & Yandong Chu & Jiangang Zhang & Yingxiang Chang & Jianning Yu & Xinlei An, 2013. "Control of Hopf Bifurcation in Autonomous System Based on Washout Filter," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:482351
    DOI: 10.1155/2013/482351
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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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