Blurring the Busse balloon: Patterns in a stochastic Klausmeier model

We investigate the effect of stochastic forcing on spatially periodic patterns in a one-dimensional Klausmeier model for dryland vegetation. Using numerical methods, we can accurately describe the transient dynamics of the stochastic solutions and compare several notions of stability. In particular, we show that the boundary of the Busse balloon - which represents the deterministically stable patterns - becomes blurred under the stochastic perturbations and that the stochastic stability heavily depends on the model parameters, the intensity of the noise and the location of the wave number of the periodic pattern within the deterministic Busse balloon.