Predictability of noise-controlled dynamics

Abstract

Noise-controlled dynamics runs counter to usual intuition: the larger the noise the more regular the solutions. We present numerical and analytical results for a set of three stochastic partial differential equations in one space dimension, motivated by the intermittent destabilization of tall thin convection cells by horizontal shear. Time-series are predictable in the sense that they follow limit cycles with a small variation in amplitude from cycle to cycle. Closer inspection reveals that the amplitude is determined by very small amounts of noise.

Onset and Synchronization of Complex Dynamic Behavior in the Light-Sensitive Belousov−Zhabotinsky Reaction with Periodic and Nearly Periodic Switching

“…A variety of studies have shown that various kinds of noise can regularize the behavior of a system. − The noisy switching times used in our study are a variation on the dichotomous (or telegraphic) noise processes studied by others. ,,− These studies have shown a variety of effects ranging from stochastic resonance 52 to stochastic coherence. ,, Our observation of synchronization in these systems is no doubt closely related to stochastic coherence. The latter phenomenon is the appearance of nontrivial structure in the coarse-grained probability density. ,, Since we can obtain similar synchronization properties with a variety of dichotomous noise processes, it seems likely that the systems we have studied will show similarly structured probability densities.…”