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Collective Order in High-dimensional Chaos

高维混沌中的集体秩序

基本信息

批准号：
07640505
负责人：
KANEKO Kunihiko
金额：
$ 1.41万
依托单位：
The University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1995
资助国家：
日本
起止时间：
1995 至 1996
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07640505/
关键词：
High-dimensional Chaos Collective Motion Turbulence Spatiotemporal Chaos Hidden Coherence Coupled Map Coupled Chaotic System Differentiation Coupled Map

项目摘要

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.

1)隐相干和集体动力学：我们分析了耦合混沌系统的集体运动。特别地，研究了具有分布非线性的全局耦合映射中的集体行为。结果表明，非均质性增强了集体动力学的规律性。这种秩序的机制是由于内部分岔结构的形成，以及结构与平均场之间的自洽动力学。我们还回顾了集体动力学及其意义，并尝试用“集体李亚普诺夫指数”来表征集体动力学。2)集体秩序即时空混沌：我们构建了一个由时空混沌产生的集体模式形成模型。空间模式被发现是由于自发对称性破缺。通过对这种转变的数值分析，我们证明了用湍流粘度对这种现象的解释在现象学上是有效的。3)耦合图气：内部混沌动力学和元素空间运动的干涉导致了一种新型的秩序，以及秩序形成和崩溃之间的流动。4)元素生灭的长期动态：通过考虑自由度的变化，我们发现元素的分化导致元素数量的增长。结果与细胞生物学的相关性也进行了讨论。