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Measuring and characterizing spatial patterns, dynamics and chaos in spatially extended dynamical systems and ecologies. (English) Zbl 0868.35055

This is a very brief survey of a number of topics related to pattern formation and spatiotemporal chaos in reaction-diffusion systems (described by nonlinear parabolic-type complex partial differential equations, a well-known example being the Ginzburg-Landau equation(s)), coupled map lattices (which are, essentially, discrete versions of the above-mentioned reaction-diffusion systems, with discretization in both temporal and spatial variables), and essentially discrete systems, such as coupled cellular automata. A very sketchy description of strange attractors amenable for the dynamical chaos and various routes to the chaos (e.g., intermittency) is given. Attention is also paid to data series analysis, data compression, extracting maximum information from data pertaining to chaotic systems, etc. Particular examples considered in the paper are taken from ecology and epidemiology.

MSC:

35K57 Reaction-diffusion equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
92D40 Ecology
92D30 Epidemiology
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