NESTED STRANGE ATTRACTORS IN SPATIOTEMPORAL CHAOTIC SYSTEMS

A self-similar fractal structure for phase-space attractors is observe d for time series produced by spatiotemporal chaotic systems. Two data sets, produced by (1) coupled logistic maps and (2) the complex Ginzb urg-Landau equation, are studied numerically. The attractor reconstruc ted in a time-delay embedding space has a coarse-grained dimension gro wing exponentially with increasing resolution. A coarse-grained K2 ent ropy in the region of scaling grows linearly with the embedding dimens ion. This type of scaling behavior is expected for developed spatiotem poral chaos in spatially homogeneous extended systems when the correla tion length is much smaller than the system size. The growth rate of t he dimension (differential dimension) is proportional to a density of dimensions and a correlation length of the system. The growth rate of K2 entropy is proportional to the entropy density and the correlation length.