Symbol statistics and spatio-temporal systems

✍ Scribed by X.Z. Tang; E.R. Tracy; R. Brown

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 645 KB
• Volume: 102
• Category: Article
• ISSN: 0167-2789
• DOI: 10.1016/s0167-2789(96)00201-1

✦ Synopsis

We consider the problem of estimating parameters from time-series observations of spatio-temporal systems. Two types of models are considered: (a) a one-dimensional coupled map lattice with nearest neighbor diffusive coupling; and (b) the complex Ginzburg-Landau equation in one and two spatial dimensions. Model parameters are to be estimated using time-series observations from only a few sites. A symbolic partition of the time series is introduced and the probabilities of observing various symbol sequences in the data are measured. The parameter fitting is accomplished by adjusting parameters of the model until it produces time series whose symbol sequences have the same probabilities as the data. We show that it is possible to reliably estimate the parameters from a single time series when the spatio-temporal dynamics is "turbulent", i.e. it displays a wide range of space and time scales with no discernible patterns.