Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multi-Delay Differential Equations: A Taylor Expansion Approach   It is already well-understood that many delay differential equations with
only a single constant delay exhibit a change in stability according to the
value of the delay in relation to a critical delay value. Finding a formula for
the critical delay is important to understanding the dynamics of delayed
systems and is often simple to obtain when the system only has a single
constant delay. However, if we consider a system with multiple constant delays,
there is no known way to obtain such a formula that determines for what values
of the delays a change in stability occurs. In this paper, we present some
single-delay approximations to a multi-delay system obtained via a Taylor
expansion as well as formulas for their critical delays which are used to
approximate where the change in stability occurs in the multi-delay system. We
determine when our approximations perform well and we give extra analytical and
numerical attention to the two-delay and three-delay settings.

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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th