Dominance of Milnor attractors in globally coupled dynamical systems with more than 7±2 degrees of freedom -: art. no. 055201
Dominance of Milnor attractors in globally coupled dynamical systems with more than 7±2 degrees of freedom -: art. no. 055201
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DOI：
10.1103/physreve.66.055201
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发表时间：
2002-11-01
影响因子：
2.4
通讯作者：
Kaneko, K
中科院分区：
文献类型：
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作者：
Kaneko, K
Milnor吸引子在一类高维动力系统中的普遍性最近被报道。我们研究了这种流行程度如何取决于自由度的数量，通过使用全球耦合的地图，并显示米尔诺吸引子的盆地分数急剧增加约5-10自由度，饱和度更高的自由度。有人认为，这种主导地位的Milnor吸引子在盆地中产生的组合爆炸的盆地边界。此外，在没有排列对称性的系统中也发现了优势，即，由不同元素组成的耦合动力系统。在心理学中可能与幻数7+/-2有关的讨论也被简要地讨论了。
The prevalence of Milnor attractors has recently been reported in a class of high-dimensional dynamical systems. We study how this prevalence depends on the number of degrees of freedom by using a globally coupled map and show that the basin fraction of Milnor attractors increases drastically around 5-10 degrees of freedom, saturating for higher numbers of degrees of freedom. It is argued that this dominance of Milnor attractors in the basin arises from a combinatorial explosion of the basin boundaries. In addition, the dominance is also found in a system without permutation symmetry, i.e., a coupled dynamical system of nonidentical elements. Possible relevance to the magic number 7+/-2 in psychology is briefly discussed.