Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Emergent Behaviors of the generalized Lohe matrix model   We present a first-order aggregation model on the space of complex matrices
which can be derived from the Lohe tensor model on the space of tensors with
the same rank and size. We call such matrix-valued aggregation model as "the
generalized Lohe matrix model". For the proposed matrix model with two cubic
coupling terms, we study several structural properties such as the conservation
laws, solution splitting property. In particular, for the case of only one
coupling, we reformulate the reduced Lohe matrix model into the Lohe matrix
model with a diagonal frustration, and provide several sufficient frameworks
leading to the complete and practical aggregations. For the estimates of
collective dynamics, we use a nonlinear functional approach using an ensemble
diameter which measures the degree of aggregation.

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The categories of this paper are: physics
28
The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
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The categories of this paper are: astro-ph