Publication detail

Periodic solutions in a linear delay difference system

ČERMÁK, J. FEDORKOVÁ, L. NECHVÁTAL, L.

English title

Periodic solutions in a linear delay difference system

Type

journal article in Web of Science

Language

en

Original abstract

The paper investigates periodicity properties of a linear autonomous difference system with two delayed terms. Assuming that the system matrices are simultaneously triangularizable, we formulate necessary and sufficient conditions guaranteeing the existence of a nonzero periodic solution (with an a priori given period) of the studied system. The analytical form of such conditions is shown to generalize the existing results on this topic. Moreover, it is supported by a geometric reformulation, offering a better understanding of the derived periodicity conditions. Information on the form of the searched periodic solution (including its prime period) is also provided.

English abstract

The paper investigates periodicity properties of a linear autonomous difference system with two delayed terms. Assuming that the system matrices are simultaneously triangularizable, we formulate necessary and sufficient conditions guaranteeing the existence of a nonzero periodic solution (with an a priori given period) of the studied system. The analytical form of such conditions is shown to generalize the existing results on this topic. Moreover, it is supported by a geometric reformulation, offering a better understanding of the derived periodicity conditions. Information on the form of the searched periodic solution (including its prime period) is also provided.

Keywords in English

difference equation; delay; periodic solution

Released

05.04.2025

Publisher

Bolyai Institute, University of Szeged

Location

Szeged

ISSN

1417-3875

Volume

2025

Number

10

Pages from–to

1–18

Pages count

18

BIBTEX


@article{BUT197855,
  author="Jan {Čermák} and Lucie {Fedorková} and Luděk {Nechvátal},
  title="Periodic solutions in a linear delay difference system",
  year="2025",
  volume="2025",
  number="10",
  month="April",
  pages="1--18",
  publisher=" Bolyai Institute, University of Szeged",
  address="Szeged",
  issn="1417-3875"
}