TY - JOUR
T1 - Local models of spatio-temporally complex fields
AU - Dankowicz, Harry
AU - Holmes, Philip
AU - Berkooz, Gal
AU - Elezgaray, Juan
N1 - Funding Information:
We would like to thank John Guckenheimear nd the refereeso f this paper for helpful criticism. This work was partially supportedb y AFOSR NM 91-0329,F 49620-92-J-0287N,A TO 92-0184,O NR N00014-94-C-0024 and DoE DE-FG02-95ER.25238.A000H.D also thanks the Swedish FulbrightC ommissiona nd the Department of Mechanics at the Royal Instituteo f Technologyi n Stockholm,S weden,for their support.
PY - 1996
Y1 - 1996
N2 - 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 rôle, certain "resonant" lengths giving superior results.
AB - 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 rôle, certain "resonant" lengths giving superior results.
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U2 - 10.1016/0167-2789(95)00245-6
DO - 10.1016/0167-2789(95)00245-6
M3 - Article
AN - SCOPUS:0000385041
SN - 0167-2789
VL - 90
SP - 387
EP - 407
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
IS - 4
ER -