J. Phys. I France
Volume 3, Numéro 2, February 1993
Page(s) 365 - 369
DOI: 10.1051/jp1:1993137
J. Phys. I France 3 (1993) 365-369

Bifurcation in a random environment

Y. Pomeau

Laboratoire de Physique Statistique, Ecole Normale Supérieure, 24 Rue Lhomond, 75231 Paris Cedex 05, France

(Received 15 May 1992, accepted in final form 30 May 1992)

I investigate various instances of bifurcation in a random stationary environment. This is done for a model equation, with a bifurcation parameter fluctuating in space. The noise is either Gaussian or two states Poisson. I estimate then the order parameter as a function of a bifurcation parameter. This is mostly done by Lifshitz-tail type estimates on the linear part of the equation. However, near the threshold of instability in the absence of noise, this one-whatever small it is-becomes important and there the nonlinearity becomes crucial too.

46.20 - 46.30L - 47.20

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