LOCAL MODELS OF SPATIO-TEMPORALLY COMPLEX FIELDS

We investigate the ability of local models of the one space dimensiona l Kuramoto-Sivashinsky partial differential equation with periodic bou ndary conditions, obtained by projection on a small set of Fourier mod es on a short subinterval, to reproduce coherent events typical of sol utions of the same equation on a much longer interval, We find that sy stems containing as few as two linearly unstable modes can produce rea listic local events in the short term, but that for more reliable shor t time tracking and long term statistics, three or four interacting mo des are required, and that the length of the short interval plays a su btle role, certain ''resonant'' lengths giving superior results.