Characterization of a system described by Kuramoto–Sivashinsky equation with Lyapunov exponent

The characteristics of a system described by Kuramoto–Sivashinsky equation are obtained through the statistics of a mean Lyapunov exponent. This mean Lyapunov exponent takes large values and fluctuates large when the system is disordered temporally and spatially. This behavior of the spatially extended system is captured clearly by the probability distribution function for the time averaged one of the mean Lyapunov exponent.