Fluctuation of mean Lyapunov exponent for Kuramoto–Sivashinsky equation

The statistical aspect of Lyapunov exponent for Kuramoto–Sivashinsky equation is studied. Fluctuation of mean Lyapunov exponent is given by the probability distribution function of its time coarse grained quantity, local Lyapunov exponent. The functional form of the probability distribution function is obtained. Its form is different from the one obtained from the large deviation statistics. Also, the relation between the damping constant included in Kuramoto–Sivashinsky equation and Lyapunov exponent is obtained.