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.

• Received 3 June 2001

DOI:https://doi.org/10.1103/PhysRevE.66.017205