MEASURING AND CHARACTERIZING SPATIAL PATTERNS, DYNAMICS AND CHAOS IN SPATIALLY EXTENDED DYNAMICAL-SYSTEMS AND ECOLOGIES

In this paper I discuss space-time chaos in both locally mixing continuum systems (reaction-diffusion equations, coupled map lattices and functional maps) and individual-based models (probabilistic cellular automata and artificial ecologies). I particularly emphasize quantification and data-analysis and attempt to address the characterization of spatial structure and dynamics in such disordered systems. I discuss the relevance of these ideas to ecology, evolution and epidemiology. The artificial ecologies I consider motivate a new definition of space-time chaos for such systems and new data analysis techniques.