K. Seki et al., SENSITIVITY TO INITIAL CONDITIONS IN STOCHASTIC-SYSTEMS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 47(1), 1993, pp. 155-163
The time evolution of the mean deviation of initially close trajectori
es in a stochastic dynamical system is investigated. It is shown both
for additive and linearly coupled multiplicative noise that the mean d
eviation loses its dependence on initial conditions for long times. Fo
r shorter times a power law is found for certain types of additive noi
se processes, in sharp contrast to the exponential separation of initi
ally nearby trajectories in deterministic chaotic systems. Exponential
time evolution is obtained for linearly coupled multiplicative noise
after an initial transient during which more complex regimes, includin
g a superexponential stage, can take place.