Volume 84, Number 3, November 2008
|Number of page(s)||6|
|Section||Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics|
|Published online||28 October 2008|
Additive noise may change the stability of nonlinear systems
INRIA CR Nancy - Grand Est, CS20101 - 54603 Villers-les-Nancy Cedex, France, EU
Corresponding author: firstname.lastname@example.org
Accepted: 24 September 2008
The present work studies the effect of additive noise on two high-dimensional systems. The first system under study is two-dimensional, evolves close to the deterministic stability threshold and exhibits an additive noise-induced shift of the control parameter when driving one variable by uncorrelated Gaussian noise. After a detailed analytical and numerical study of this effect, the work further focusses on the extended Swift-Hohenberg equation subjected to global noise, i.e. noise constant in space and uncorrelated in time. This spatial system generalizes the two-dimensional system and thus reveals phase transitions induced by additive global noise. Numerical studies confirm this effect. Further closer investigations reveal that the occurence of the noise-induced shift is subjected to the model nonlinearity and the shifts sign depends on the sign of the nonlinearity prefactors.
PACS: 47.54.-r – Pattern selection; pattern formation / 02.50.Ey – Stochastic processes / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion
© EPLA, 2008
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