Local models of spatio-temporally complex fields

We investigate the ability of local models of the one space dimensional Kuramoto-Sivashinsky partial differential equation with periodic boundary conditions, obtained by projection on a small set of Fourier modes on a short subinterval, to reproduce coherent events typical of solutions of the same equation on a much longer interval, We find that systems containing as few as two linearly unstable modes can produce realistic local events in the short term, but that for more reliable short time tracking and long term statistics, three or four interacting modes are required, and that the length of the short interval plays a subtle role, certain ''resonant'' lengths giving superior results.