Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Periodic Cluster Attractors and their Stabilities in the Turbulent
  Globally Coupled Map Lattice   The Globally Coupled Map Lattice (GCML) is one of the basic model of the
intelligence activity. We report that, in its so-called turbulent regime,
periodic windows of the element maps foliate and systematically control the
dynamics of the model. We have found various cluster attractors. In one type of
them, the maps split into several almost equally populated clusters and the
clusters mutually oscillate with a period (p) that is the same with the number
of clusters (c). We name them as maximally symmetric cluster attractors
(MSCA's). The most outstanding are the p3c3 MSCA and its bifurcate. The MSCA is
proved to be linearly stable by Lyapunov analysis. There are also cluster
attractors with p>c. They come out in sequences with increasing coupling. The
formation of the clustors in the very weakly coupled chaotic system may suggest
a new form of an intelligence activity.

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The categories of this paper are: math-ph
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The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
1
The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat