Estimation of intensive quantities in spatio-temporal systems from time-series

We study multivariate time-series generated by coupled map lattices exhibit ing spatio-temporal chaos and investigate to what extent we are able to est imate various intensive measures of the underlying system without explicit knowledge of the system dynamics. Using the rescaling and interleaving prop erties of the Lyapunov spectrum of systems in a spatio-temporally chaotic r egime and paying careful attention to errors introduced by sub-system bound ary effects, we develop algorithms that are capable of estimating the Lyapu nov spectrum from time-series. We analyse the performance of these and find that the choice of basis used to fit the dynamics is crucial: when the loc al dynamics at a lattice site is well approximated by this basis we are abl e to accurately determine the full Lyapunov spectrum. However, as the local dynamics moves away from the space spanned by this basis, the performance of our algorithm deteriorates. (C) 2000 Elsevier Science B.V. All rights re served.