Extensive chaos in the nikolaevskii model

We carry out a systematic study of a different type of chaos at onset ("soft-mode turbulence") based on numerical integration of the simplest one-dimensional model. The chaos is characterized by a smooth interplay of different spatial scales, with defect generation being unimportant. The Lyapunov exponents are calculated for several system sizes for fixed values of the control parameter epsilon. The Lyapunov dimension and the Kolmogorov-Sinai entropy are calculated and both shown to exhibit extensive and microextensive scaling. The distribution functional is shown to satisfy Gaussian statistics at small wave numbers and small frequency.