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Pattern formation in two-dimensional arrays of coupled, discrete-time oscillators.

The nature of stable, inhomogeneous patterns and the character of the evolution to such attracting states is studied for a model dynamical system consisting of a two-dimensional array of coupled, discrete-time oscillators. The orbit scaling structure of a single quadratic map can be transcribed onto the map parameter-coupling parameter plane for the homogeneous states arising from subharmonic bifurcations in the coupled-map array. The study of the evolution of various types of initial inhomogeneity shows how the different patterns arise, some of which resemble those observed in physical systems. Some features of the evolution process can be understood in terms of the stability analysis about the homogeneous state.