Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2004-08-14
Phys. Rev. E 70, 036215 (2004)
Nonlinear Sciences
Pattern Formation and Solitons
11 pages, 13 figures, to be published in Pre. Rev. E
Scientific paper
10.1103/PhysRevE.70.036215
We develop a hierarchical structure (HS) analysis for quantitative description of statistical states of spatially extended systems. Examples discussed here include an experimental reaction-diffusion system with Belousov-Zhabotinsky kinetics, the two-dimensional complex Ginzburg-Landau equation and the modified FitzHugh-Nagumon equation, which all show complex dynamics of spirals and defects. We demonstrate that the spatial-temporal fluctuation fields in the above mentioned systems all display the HS similarity property originally proposed for the study of fully developed turbulence [Z.-S. She and E. Leveque, Phys. Rev. Lett. {\bf 72}, 336 (1994)]. The derived values of a HS parameter $\beta$ from experimental and numerical data in various physical regimes exhibit consistent trends and characterize the degree of turbulence in the systems near the transition, and the degree of heterogeneity of multiple disorders far from the transition. It is suggested that the HS analysis offers a useful quantitative description for the complex dynamics of two-dimensional spatiotemporal patterns.
Guo Hongyu
Li Liang
Liu Jian
Ouyang Qi
She Zhen-Su
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