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Additive noise may change the stability of nonlinear systems

Axel Hutt 1 
1 CORTEX - Neuromimetic intelligence
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
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.
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Submitted on : Friday, July 3, 2009 - 12:05:37 PM
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Axel Hutt. Additive noise may change the stability of nonlinear systems. EPL - Europhysics Letters, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2008, 84 (3), ⟨10.1209/0295-5075/84/34003⟩. ⟨inria-00401522⟩



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