Universal behavior of coupled nonlinear systems

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Abstract
Using renormalization theory it is shown that systems of coupled maps can be characterized with a few universality groups. Identical maps with quadratic maxima, linearly coupled, exhibit α and δ scaling in the parameter space of coupling strength and amplitude of the uncoupled maps. Nonlinear coupling leads to 2 and δ scaling in the same parameter space. Systems with degenerate coupling, where the coupling terms have the same form as the uncoupled maps, show special features. Examples for two coupled maps, and many maps with nearest-neighbor coupling as well as mean-field coupling are worked out and scaling is demonstrated.