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Pattern dynamics in spatiotemporal chaos. Pattern selection, diffusion of defect and pattern competition intermittency. (English) Zbl 0702.58043

From the abstract: “A class of coupled map lattices is investigated as a model for the spatiotemporal chaos. As the parameters are changed, phase transitions among the patterns are observed. Pattern selection through the chaotic motion of domain is observed. Chaos is suppressed by the selection. Selection of the zigzag pattern is studied, where localized defects which separate the two anti-phase domains are found. They change chaotically in time and move randomly in space. The diffusion of defect is related with its chaotic motion. Collapse of zigzag pattern and the defect turbulence are studied in connection with the crisis in high- dimensional dynamical systems. Pattern selection with longer wavelengths is found in the stronger coupling regime. Transition from pattern selection phase to fully developed turbulence occurs via the intermittency. Selective flicker-like noise and the Pareto distribution of lifetime of pattern are observed at the intermittency regime. For the quantitative characterization of each phase, pattern distributions, pattern transition matrix, static and dynamical entropies, lifetime distribution of pattern, spatiotemporal power spectra, and Lyapunov spectra are calculated. Phase transition from the pattern selection to fully developed turbulence is investigated with the use of these quantifiers, where some order parameters and critical indices are introduced.”
Reviewer: K.Brod

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37G99 Local and nonlocal bifurcation theory for dynamical systems
58C05 Real-valued functions on manifolds
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