SPATIOTEMPORAL CHAOS - A SOLVABLE MODEL

A solvable coupled map lattice model exhibiting spatio-temporal chaos is studied. Exact expressions are obtained for the spectra of Lyapunov exponents as a function of the model parameters. Although the model h as spatio-temporal structure, the time series measured at a single lat tice site are shown to consist of independent, identically distributed samples for several values of the model parameters. For these paramet er values, the spatial series measured at a fixed time also consist of independent, identically distributed samples. In these cases, the inf ormation dimension density is 1, but the information entropy density d epends on the model parameters. Thus, the model is an example where th e information entropy density can be obtained neither from a time seri es measured at a single lattice site nor from a spatial series measure d at a fixed time, We conclude that in studying only a time series or a spatial series without any knowledge of the system, one could be eas ily led into thinking that there is no spatio-temporal structure. For a full characterization of the system, structure in time and space wil l have to be considered simultaneously.