The escape problem and inverse stochastic resonance in a two-dimensional airfoil system driven by fractional Gaussian noise

Aircraft wings encounter complex stochastic loads during flight that traditional Gaussian white noise models inadequately represent. This paper examines a two-dimensional airfoil with nonlinear pitching stiffness subjected to fractional Gaussian noise, employing the Hurst index parameter to simulate the complex random loads experienced by wing structures during flight. Our results reveal significant inverse stochastic resonance, characterized by oscillation suppression at intermediate noise intensities. Anti-persistent noise ($H<0.5$) requires higher intensities for optimal suppression while persistent noise ($H>0.5$) shows minimal ISR profile variation. To understand the underlying mechanisms of this phenomenon, we conduct escape time analysis between fixed points and limit cycles. Both mean first passage time analysis and probability density functions establish an exponential relationship between transition times and noise intensity that persists across different Hurst indices, despite the non-Markovian nature of the noise. These findings provide valuable insights for airfoil system design in realistic turbulent environments.