Spatiotemporal chaos in spatially extended systems

To address finite-size effects in the use of the decay mutual information to characterize spatiotemporal chaotic dynamics, we modify the dispersion of the nonlinear Schrödinger equation to obtain a model system for which the number of unstable modes remains fixed while the domain size increases. Our numerical study of the model system clearly establishes that spatiotemporal chaos arises in the presence of only two unstable modes. In this spatially extended system, the spatiotemporal chaos is characterized by chaotic dynamics in time and by an exponential decay in space of mutual information, with the decay rate becoming system-size independent in the large system-size limit.