Nonlinear Dynamics

, Volume 67, Issue 4, pp 2637–2649 | Cite as

Supercritical and subcritical Hopf bifurcation and limit cycle oscillations of an airfoil with cubic nonlinearity in supersonic\hypersonic flow

  • Hulun Guo
  • Yushu Chen
Original Paper


In this paper, the Hopf bifurcations and limit cycle oscillations (LCOs) of an airfoil with cubic nonlinearity in supersonic\hypersonic flow are investigated. The harmonic balance method and multivariable Floquet theory are applied to analyze the LCOs of the airfoil. Four distinct cases of the LCOs response are detected in this system: (I) supercritical Hopf bifurcation, (II) a single subcritical Hopf bifurcation, (III) two subcritical Hopf bifurcations, and (IV) no Hopf bifurcation. Furthermore, the parameter variations domains separating the supercritical and subcritical Hopf bifurcations are presented using singularity theory.


Supercritical and subcritical Hopf bifurcation LCO Harmonic balance method Floquet theory Singularity theory 


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.School of AstronauticsHarbin Institute of TechnologyHarbinChina

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