Fluctuation of mean Lyapunov exponent for turbulence

Lyapunov exponent for the systems described by the complex Ginzburg–Landau equation is studied through its statistics. The probability distribution function for the finite-time-average Lyapunov exponent is given. Its functional form is the same as the systems described by the Kuramoto–Sivashinsky equation that expresses the weak turbulence. It is predicted that many kinds of turbulence have the same characteristics concerning their statistics of Lyapunov exponent.