Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiplicity-induced-dominancy for delay-differential equations of
  retarded type   An important question of ongoing interest for linear time-delay systems is to
provide conditions on its parameters guaranteeing exponential stability of
solutions. Recent works have explored spectral techniques to show that, for
some low-order delay-differential equations of retarded type, spectral values
of maximal multiplicity are dominant, and hence determine the asymptotic
behavior of the system, a property known as multiplicity-induced-dominancy.
This work further explores such a property and shows its validity for general
linear delay-differential equations of retarded type of arbitrary order
including a single delay in the system's representation. More precisely, an
interesting link between characteristic functions with a real root of maximal
multiplicity and Kummer's confluent hypergeometric functions is exploited. We
also provide examples illustrating our main result.

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The categories of this paper are: cs
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: eess