Partition complexity in a network of chaotic elements

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Abstract
A network of chaotic elements is investigated with the use of globally coupled maps. Elements can split into clusters with synchronized oscillation. In a partially ordered phase, the clustering has an inhomogeneous tree structure like replica symmetry breaking in spin glass. The clustering has large variety by attractors and strongly depends on initial conditions. The variety of clusterings is characterized by the distribution of partitions originated in spin glass theory. The qualitative similarity and quantitative disagreement of the given attractors with a spin glass are clarified.