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

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)

Abstract
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.

PACS
46.20 - 46.30L - 47.20

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