Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Critical Delays and Polynomial Eigenvalue Problems   In this work we present a new method to compute the delays of delay
differential equations (DDEs), such that the DDE has a purely imaginary
eigenvalue. For delay differential equations with multiple delays, the critical
curves or critical surfaces in delay space (that is, the set of delays where
the DDE has a purely imaginary eigenvalue) are parameterized. We show how the
method is related to other works in the field by treating the case where the
delays are integer multiples of some delay value, i.e., commensurate delays.
  The parametrization is done by solving a {\em quadratic eigenvalue problem}
which is constructed from the vectorization of a matrix equation and hence
typically of large size. For commensurate delay differential equations, the
corresponding equation is a polynomial eigenvalue problem. As a special case of
the proposed method, we find a closed form for a parameterization of the
critical surface for the scalar case.
  We provide several examples with visualizations where the computation is done
with some exploitation of the structure of eigenvalue problems.

27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn