Nonstatistical behavior of higher-dimensional coupled systems

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Abstract
We study a (generalized) globally coupled system whose elements are two-dimensional chaotic maps, and find clear evidence of nonstatistical behavior: the mean-square deviation (MSD) of both components of the mean field saturate with respect to an increase in the number of coupled elements, N, after a critical value of N is reached, and their distributions are clearly non-Gaussian. We also find that the power spectrum of both components of the mean field display well-defined peaks, indicating a subtle coherence among different elements, even in the ‘‘turbulent’’ phase. This system is a higher-dimensional example of coupled maps, and its study confirms that the phenomena observed in a wide class of coupled one-dimensional maps (and also in an example of coupled complex maps) are present here as well. This gives more evidence to support that such nonstatistical behavior is probably generic in globally coupled systems. We also investigate the influence of parametric fluctuations on the MSD and power spectra, and find that noise restores the statistical behavior, after a critical value of the number of coupled elements is reached.