SENSITIVITY TO INITIAL CONDITIONS IN STOCHASTIC-SYSTEMS

The time evolution of the mean deviation of initially close trajectories in a stochastic dynamical system is investigated. It is shown both for additive and linearly coupled multiplicative noise that the mean deviation loses its dependence on initial conditions for long times. For shorter times a power law is found for certain types of additive noise processes, in sharp contrast to the exponential separation of initially 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, including a superexponential stage, can take place.