Spatial and temporal spectra of noise driven stripe patterns

Abstract

Spatial and temporal noise power spectra of stripe patterns are investigated, using as a model a Swift-Hohenberg equation with a stochastic term. In particular, the analytical and numerical investigations show: (1) the temporal noise spectra are of ${1/f}^{\alpha }$ form, where $\alpha =1+\left(3\mathrm{}-D\right)/4\mathrm{}$ with D the spatial dimension of the system; (2) that the stochastic fluctuations of the stripe position are subdiffusive.