Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic flocking in the Cucker-Smale model with reaction-type delays
  in the non-oscillatory regime   We study a variant of the Cucker-Smale system with reaction-type delay. Using
novel backward-forward and stability estimates on appropriate quantities we
derive sufficient conditions for asymptotic flocking of the solutions. These
conditions, although not explicit, relate the velocity fluctuation of the
initial datum and the length of the delay. If satisfied, they guarantee
monotone decay (i.e., non-oscillatory regime) of the velocity fluctuations
towards zero for large times. For the simplified setting with only two agents
and constant communication rate the Cucker-Smale system reduces to the delay
negative feedback equation. We demonstrate that in this case our method
provides the sharp condition for the size of the delay such that the solution
be non-oscillatory. Moreover, we comment on the mathematical issues appearing
in the formal macroscopic description of the reaction-type delay system.

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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: gr-qc