An Isaac Newton Institute Workshop

Developments in Experimental Pattern Formation

Effect of multiplicative noise on instabilities

Author: Fauve (ENS-LPS)

Abstract

It has been known for a long time that random fluctuations of the control parameters of a dynamical system, or multiplicative noise, may generate surprising effects, such as stabilization by noise, noise induced transitions, etc. Multiplicative noise can also modify scaling laws in the vicinity of bifurcation thresholds. We present an experimental study of the effect of noise on surface waves generated by vertically vibrating a layer of fluid (the Faraday instability). We show that multiplicative noise can both enhance or inhibit the instability and emphasize the differences between amplitude, frequency and phase noise. In the later case, we show that a deterministic amplitude equation can be derived, with coefficients renormalized by noise. In the former cases, we discuss the phenomenon of on-off intermittency. Finally, we present some other instability problemsinvolving fluctuations in time or space acting like a multiplicative noise.