大域的結合写像素子系の乱流領域における周期的集団運動

概要

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Systematic appearance of collective periodic motions of maps is investigated in the turbulent regime of the globally coupled map lattice (GCML). Previously it was thought that this is a region of randomly evolving chaotic maps under a weak correlation called a hidden coherence. In this note it is shown by ample numerical evidences that the turbulent regime is in fact a region dominated by the successive manifestation of collective motions with various periodicity which are respectively related to the periodic windows of a single logistic map. An analytic scale transformation of maps, valid for maximally symmetric periodic clusters, is shown to be a vital tool to keep track of the reduction of GCML dynamics. By a statistical analysis of the large size limit of the model, the hidden coherence is located in some limited regions, which we call valleys of the mean-squared-deviation surface.
明治大学の論文