The effect of multiplicative noise on the relaxation time of a real non-linear physical system: a comparison of experiment and theory for the random growing rate model (RGRM)

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Abstract
It is found that the theoretical behaviour of the relaxation time T for the random growing rate model (RGRM) under the influence of multiplicative noise of intensity Q (a monotonic decrease of T-1 towards a limiting value as Q to infinity ) differs markedly from that actually measured in electronic simulators of that system. A new electronic analogue experiment is described in which a distinct minimum in T-1(Q) has been observed for the first time, with clear evidence for an increase of T-1(Q) with Q at large Q in good qualitative agreement with an earlier analogue experiment. The discrepancy between experiment and the theoretical solutions of the (idealised) equation is attributed to the profound influence exerted by the very weak additive noise which must also, in some measure, always be present in a real physical system.