One goal is to find evidence of determinism in such data. An Example is a 2-D quadratic map. Models developed to fit chaotic data are seldom chaotic. The Mandelbrot set is chaotic almost nowhere. It has a very complicated basin boundary.
Maps become less and flows more chaotic as dimension increases.
Artificial neural networks are another kind of iterated map. Neural networks become more chaotic as dimension increases. There are many types of attractors. Strange attractors are produced by a stretching and folding. Attractor dimension increases with system dimension.