Hopf bifurcation for a fractional van der Pol oscillator and applications to aerodynamics: implications in flutter

Abstract Flutter is an important instability in aeroelasticity. In this work,we derive a model for phenomenon which naturally leads to equation similar van der Pol oscillator the friction term given by fractional derivative. Motivated these considerations,we study and show that it exhibits Hopf bifurcation. The based on one-dimensional reduction where instabilities associated with flutter are preserved. However, due derivative, bifurcation analysis differs from standard case. We present both analytical numerical results discuss implications aerodynamics. Additionally, we contrast our qualitative experimental data.