Microextensive Chaos of a Spatially Extended System

Details Microextensive Chaos of a Spatially Extended System Microextensive Chaos of a Spatially Extended System

2001-06-04

arxiv.org/abs/nlin/0106002v1

Nonlinear Sciences

Pattern Formation and Solitons

5 pages including 4 figures. Submitted to PRE

Scientific paper

10.1103/PhysRevE.66.017205

By analyzing chaotic states of the one-dimensional Kuramoto-Sivashinsky equation for system sizes L in the range 79 <= L <= 93, we show that the Lyapunov fractal dimension D scales microextensively, increasing linearly with L even for increments Delta{L} that are small compared to the average cell size of 9 and to various correlation lengths. This suggests that a spatially homogeneous chaotic system does not have to increase its size by some characteristic amount to increase its dynamical complexity, nor is the increase in dimension related to the increase in the number of linearly unstable modes.

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