Predictability of noise-controlled dynamics
Centre for Nonlinear Studies
Los Alamos National Laboratory
University of Cambridge
Cambridge, CB3 9EW, UK.
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 destabilisation 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.