Quantitative characterization of spatiotemporal chaos

In this paper one way to characterize spatiotemporal chaos is shown. A coupled map lattice is used as a model for the spatiotemporal chaos. The local expansion rate is defined for the coupled map lattice in the extension of the low-dimensional temporal chaos. It is shown that the local expansion rate is closely related to the spatiotemporal pattern of the spatiotemporal chaos. The thermodynamic formalism is applied to the local expansion rate. The thermodynamic functions describing fluctuations of the local expansion rate are shown. The spatiotemporal pattern that fluctuates is shown at the same time. It is shown clearly that the thermodynamic functions characterize the spatiotemporal chaos.