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Nested strange attractors in spatiotemporal chaotic systems

Journal Article · · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States)
 [1]
  1. Institute for Nonlinear Science, University of California, San Diego, California 92093-0402 (United States)
+ Show Author Affiliations

A self-similar fractal structure for phase-space attractors is observed for time series produced by spatiotemporal chaotic systems. Two data sets produced by (1) coupled logistic maps and (2) the complex Ginzburg-Landau equation are studied numerically. The attractor reconstructed in a time-delay embedding space has a coarse-grained dimension growing exponentially with increasing resolution. A coarse-grained [ital K][sub 2] entropy in the region of scaling grows linearly with the embedding dimension. This type of scaling behavior is expected for developed spatiotemporal chaos in spatially homogeneous extended systems when the correlation length is much smaller than the system size. The growth rate of the dimension (differential dimension) is proportional to a density of dimensions and a correlation length of the system. The growth rate of [ital K][sub 2] entropy is proportional to the entropy density and the correlation length.

DOE Contract Number:
FG03-90ER14138
OSTI ID:
5835889
Journal Information:
Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States), Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States) Vol. 48:5; ISSN PLEEE8; ISSN 1063-651X
Country of Publication:
United States
Language:
English

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Related Subjects

661100* -- Classical & Quantum Mechanics-- (1992-)
665000 -- Physics of Condensed Matter-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ATTRACTORS
ENTROPY
FRACTALS
GINZBURG-LANDAU THEORY
MATHEMATICAL SPACE
MATHEMATICS
NUMERICAL SOLUTION
PHASE SPACE
PHYSICAL PROPERTIES
SCALING LAWS
SPACE
STOCHASTIC PROCESSES
THERMODYNAMIC PROPERTIES
TIME-SERIES ANALYSIS