Issue
EPL
Volume 84, Number 3, November 2008
Article Number 34003
Number of page(s) 6
Section Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics
DOI http://dx.doi.org/10.1209/0295-5075/84/34003
Published online 28 October 2008
EPL, 84 (2008) 34003
DOI: 10.1209/0295-5075/84/34003

Additive noise may change the stability of nonlinear systems

A. Hutt

INRIA CR Nancy - Grand Est, CS20101 - 54603 Villers-les-Nancy Cedex, France, EU

axel.hutt@loria.fr

received 23 May 2008; accepted in final form 24 September 2008; published November 2008
published online 28 October 2008

Abstract
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