Spectra of evolution operators of a class of neutral renewal equations: Theoretical and numerical aspects

Dimitri Breda; Davide Liessi; Sjoerd M. Verduyn Lunel

doi:10.1016/j.apnum.2023.06.018

Spectra of evolution operators of a class of neutral renewal equations: Theoretical and numerical aspects

Dimitri Breda, Davide Liessi^*, Sjoerd M. Verduyn Lunel

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

In this work we begin a theoretical and numerical investigation on the spectra of evolution operators of neutral renewal equations, with the stability of equilibria and periodic orbits in mind. We start from the simplest form of linear periodic equation with one discrete delay and fully characterize the spectrum of its monodromy operator. We perform numerical experiments discretizing the evolution operators via pseudospectral collocation, confirming the theoretical results and giving perspectives on the generalization to systems and to multiple delays. Although we do not attempt to perform a rigorous numerical analysis of the method, we give some considerations on a possible approach to the problem.

Original language	English
Pages (from-to)	124-137
Number of pages	14
Journal	Applied Numerical Mathematics
Volume	200
DOIs	https://doi.org/10.1016/j.apnum.2023.06.018
Publication status	Published - Jun 2024

Bibliographical note

Publisher Copyright:
© 2023 IMACS

Funding

This work was partially supported by the Italian Ministry of University and Research (MUR) through the PRIN 2020 project (No. 2020JLWP23) "Integrated Mathematical Approaches to Socio-Epidemiological Dynamics" (CUP: E15F21005420006). The work of Davide Liessi was partially supported by Finanziamento Giovani Ricercatori 2018-2019 and 2020-2021 of INdAM Research group GNCS.

Funders	Funder number
Italian Ministry of University and Research (MUR) through the PRIN 2020 project "Integrated Mathematical Approaches to Socio-Epidemiological Dynamics"	2020JLWP23, CUP: E15F21005420006
Finanziamento Giovani Ricercatori 2018-2019
The 2020-2021 of INdAM Research group GNCS

Keywords

Evolution operators
Monodromy operators
Pseudospectral collocation
Spectral analysis

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10.1016/j.apnum.2023.06.018

1-s2.0-S0168927423001836-mainFinal published version, 489 KBLicence: Taverne

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abstract = "In this work we begin a theoretical and numerical investigation on the spectra of evolution operators of neutral renewal equations, with the stability of equilibria and periodic orbits in mind. We start from the simplest form of linear periodic equation with one discrete delay and fully characterize the spectrum of its monodromy operator. We perform numerical experiments discretizing the evolution operators via pseudospectral collocation, confirming the theoretical results and giving perspectives on the generalization to systems and to multiple delays. Although we do not attempt to perform a rigorous numerical analysis of the method, we give some considerations on a possible approach to the problem.",

keywords = "Evolution operators, Monodromy operators, Pseudospectral collocation, Spectral analysis",

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year = "2024",

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doi = "10.1016/j.apnum.2023.06.018",

language = "English",

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AU - Breda, Dimitri

AU - Liessi, Davide

AU - Verduyn Lunel, Sjoerd M.

PY - 2024/6

Y1 - 2024/6

N2 - In this work we begin a theoretical and numerical investigation on the spectra of evolution operators of neutral renewal equations, with the stability of equilibria and periodic orbits in mind. We start from the simplest form of linear periodic equation with one discrete delay and fully characterize the spectrum of its monodromy operator. We perform numerical experiments discretizing the evolution operators via pseudospectral collocation, confirming the theoretical results and giving perspectives on the generalization to systems and to multiple delays. Although we do not attempt to perform a rigorous numerical analysis of the method, we give some considerations on a possible approach to the problem.

AB - In this work we begin a theoretical and numerical investigation on the spectra of evolution operators of neutral renewal equations, with the stability of equilibria and periodic orbits in mind. We start from the simplest form of linear periodic equation with one discrete delay and fully characterize the spectrum of its monodromy operator. We perform numerical experiments discretizing the evolution operators via pseudospectral collocation, confirming the theoretical results and giving perspectives on the generalization to systems and to multiple delays. Although we do not attempt to perform a rigorous numerical analysis of the method, we give some considerations on a possible approach to the problem.

KW - Evolution operators

KW - Monodromy operators

KW - Pseudospectral collocation

KW - Spectral analysis

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VL - 200

SP - 124

EP - 137

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

ER -

Spectra of evolution operators of a class of neutral renewal equations: Theoretical and numerical aspects

Abstract

Bibliographical note

Funding

Keywords

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