Asymptotic Behaviour of Coupled Systems in Discrete and Continuous Time

Lassi Paunonen; David Seifert

doi:10.1007/s10884-016-9547-1

Asymptotic Behaviour of Coupled Systems in Discrete and Continuous Time

Lassi Paunonen, David Seifert

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

4 Citations (Scopus)

21 Downloads (Pure)

Abstract

This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for initial values satisfying a slightly stronger condition we obtain an optimal estimate on the rate of convergence. By establishing a connection with a related problem in continuous time, we are able to use this optimal estimate to improve the rate of convergence in the continuous setting obtained by the authors in a previous paper. We illustrate the power of the general approach by using it to study several concrete examples, both in continuous and in discrete time.

Original language	English
Pages (from-to)	433-445
Number of pages	13
Journal	JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
Volume	30
Issue number	2
Early online date	22 Aug 2016
DOIs	https://doi.org/10.1007/s10884-016-9547-1
Publication status	Published - Jun 2018
Publication type	A1 Journal article-refereed

Keywords

$C_0$-semigroups
Asymptotic behaviour
Power-boundeness
Rates of convergence
Recurrence relations
Spectral theory
System

Publication forum classification

Publication forum level 2

ASJC Scopus subject areas

Analysis

Access to Document

10.1007/s10884-016-9547-1

Author accepted manuscript
The final publication is available at Springer via http://dx.doi.org/10.1007/s10884-016-9547-1
Accepted author manuscript, 187 KBLicence: CC BY-NC-ND

http://urn.fi/URN:NBN:fi:tty-201709191892

1 Visit abroad

University of Oxford
Paunonen, L. (Visitor)
7 Mar 2016 → 6 Apr 2016
Activity: Visiting an external institution › Visit abroad

4 Citations
1 Conference contribution

Asymptotic Behaviour of Platoon Systems
Paunonen, L. & Seifert, D., Jul 2016, Proceedings of the 22nd International Symposium on Mathematical Theory of Networks and Systems. University of Minnesota, p. 830-836 7 p.
Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Scientific › peer-review

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abstract = "This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for initial values satisfying a slightly stronger condition we obtain an optimal estimate on the rate of convergence. By establishing a connection with a related problem in continuous time, we are able to use this optimal estimate to improve the rate of convergence in the continuous setting obtained by the authors in a previous paper. We illustrate the power of the general approach by using it to study several concrete examples, both in continuous and in discrete time.",

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AU - Seifert, David

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AB - This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for initial values satisfying a slightly stronger condition we obtain an optimal estimate on the rate of convergence. By establishing a connection with a related problem in continuous time, we are able to use this optimal estimate to improve the rate of convergence in the continuous setting obtained by the authors in a previous paper. We illustrate the power of the general approach by using it to study several concrete examples, both in continuous and in discrete time.

KW - $C_0$-semigroups

KW - Asymptotic behaviour

KW - Power-boundeness

KW - Rates of convergence

KW - Recurrence relations

KW - Spectral theory

KW - System

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DO - 10.1007/s10884-016-9547-1

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IS - 2

ER -

Asymptotic Behaviour of Coupled Systems in Discrete and Continuous Time

Abstract

Keywords

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ASJC Scopus subject areas

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University of Oxford

Research output

Asymptotic Behaviour of Platoon Systems

Cite this