Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Insights into the multiplicity-induced-dominancy for scalar
  delay-differential equations with two delays   It has been observed in recent works that, for several classes of linear
time-invariant time-delay systems of retarded or neutral type with a single
delay, if a root of its characteristic equation attains its maximal
multiplicity, then this root is the rightmost spectral value, and hence it
determines the exponential behavior of the system, a property usually referred
to as multiplicity-induced-dominancy (MID). In this paper, we investigate the
MID property for one of the simplest cases of systems with two delays, a scalar
delay-differential equation of first order with two delayed terms of order
zero. We discuss the standard approach based on the argument principle for
establishing the MID property for single-delay systems and some of its
limitations in the case of our simple system with two delays, before proposing
a technique based on crossing imaginary roots that allows to conclude that the
MID property holds in our setting.

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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph