Coupled maps with local and global interactions

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Abstract
A coupled map lattice model with both local and global couplings is studied as a simple example of hierarchical pattern dynamics with different length scales of interactions. Several phases are classified according to domain structures, degree of chaotic dynamics, distribution function, and power spectra. In particular, a cascade process of formation and collapse of bubbles is found in some parameter regime. The state is characterized by spatiotemporal power-law correlation and few positive Lyapunov exponents. In a two-dimensional case, the state leads to a characteristic spatiotemporal pattern that may be regarded as a dynamic extension of a Turing pattern. The possible relevance to natural patterns is also discussed.

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