Article ID Journal Published Year Pages File Type
1897466 Physica D: Nonlinear Phenomena 2006 19 Pages PDF
Abstract

Effects of a frozen random contribution to the control parameter are investigated in terms of the complex Ginzburg–Landau equation with real coefficients. The threshold of the bifurcation from the homogeneous basic state is reduced by a random contribution even with a vanishing spatial mean value, as shown by three different approaches, by a perturbation calculation, by a self-consistent iteration method and by a fully numerical solution of the linear part of the Ginzburg–Landau equation. For arbitrary random contributions the nonlinear stationary solutions are numerically determined and in the limit of small random amplitudes analytical expressions are derived in terms of two different perturbation expansions, which cover already several related trends beyond threshold. For instance, the spatial modulations of the solutions increase with the noise amplitude, but decrease with increasing distance from threshold.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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