Collective Order in High-dimensional Chaos

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1) hidden coherence and collective dynamics : We have analyzed collective motion of coupled chaotic systems. In particular, collective behavior is studied in globally coupled maps with distributed nonlinearity. It is shown that the heterogeneity enhances regularity in the collective dynamics.The mechanism of this order is due to the formation of an internal bifurcation structure, and the self-consistent dynamics between the structures and the mean-field. We have also reviewed the colletcive dynamics and its significance, with some attempts of the characterization by "collective Lyapunove exponent".2) Colletcive order is spatiotemporal chaos : We have constrcuded a model of collective pattern formation arising from spatiotemporal chaos. The spatial pattern is found to be due to spontaneous symmetry breaking. Through numerical analysis of the transition, we have shown that the interpretation of the phenomenon by the turbluent visocity is valid phenomenologically.3) Coupled map gas : The interferrence of internal caotic dynamics and the spatial motion of elements leads to a novel type of order, and the itinerancy between the order formation and collapse.4) Long-term dynamics with the birth and death of elements : By allowing for the change of degrees of freedom, we have found that the differentiation of elements leads to the growth in number of elements. Relevance of the results to cell biology is also discussed.