The movement of an airfoil under a steady, uniform incoming flow modelled as a 2 degree-of-freedom, pitch-plunge system is a classical model. The lift force and the moment on the airfoil are derived using the Wagner function formulation. The springs in both the pitch and the plunge directions are considered to be non-linear to allow for large deformations. The non-linear springs are assumed to be soft-springs, which gives rise to hysteresis in the long-term behaviour of the system when the reduced velocity of the incoming flow is varied. The subcritical bifurcation gives rise to a multi-stable region where the system is sensitive to external noise. The presence of noise alters the dynamical behaviour of the system considerably when compared to the deterministic system. Characterizing the output of the stochastic system through their joint probability density functions, we study the stochastic bifurcations and the manifestation of the phenomenon of stochastic resonance in the noisy system. The study can be extended by considering the effect of both the additive and parametric noise on the system. Also we look to develop measures based on the networks generated by converting the resulting time series into complex networks.