Eur. Phys. J. B 51, 357-362 (2006)
https://doi.org/10.1140/epjb/e2006-00236-4

Modification of instability processes by multiplicative noises

Laboratoire de Physique Statistique, École Normale Supérieure, CNRS UMR 8550, 24 rue Lhomond, 75005 Paris, France

Corresponding author: ^a petrelis@lps.ens.fr

Received: 28 September 2005
Revised: 13 January 2006
Published online: 14 June 2006

Abstract

We study two dynamical systems submitted to white and Gaussian random noise acting multiplicatively. The first system is an imperfect pitchfork bifurcation with a noisy departure from onset. The second system is a pitchfork bifurcation in which the noise acts multiplicatively on the non-linear term of lowest order. In both cases noise suppresses some solutions that exist in the deterministic regime. Besides, for the first system, the imperfectness of the bifurcation reduces the regime of on-off intermittency. For the second system, the unstable mode can achieve a jump of finite amplitude at instability but without hysteresis. We finally identify a generic property that is verified by the stationary probability density function of the dynamical variable when a control parameter is varied.