Publication result detail

Planar linear differential weakly delayed systems with constant matrices and equivalent ordinary differential systems

DEREVIANKO, A.; DIBLÍK, J.

Original Title

Planar linear differential weakly delayed systems with constant matrices and equivalent ordinary differential systems

English Title

Planar linear differential weakly delayed systems with constant matrices and equivalent ordinary differential systems

Type

WoS Article

Original Abstract

Considered is a linear planar delayed differential system x(center dot)(t) = Ax(t) + Bx(t-tau), where t >= 0, tau > 0 is a constant delay and A, Bare 2 x 2 constant matrices. Assuming that the system is weakly delayed, its general solution is constructed utilizing the Laplace transform. All the cases are specified of the solutions merging. Moreover, ordinary differential systems are considered such that general solutions of both delayed and non-delayed systems coincide when a transient interval is passed. Initial data for the relevant non-delayed systems are used such that these define the same solution as the corresponding initial data to the delayed system. An analysis of previous findings is given with two illustrative examples considered. Some open problems are suggested as well.

English abstract

Considered is a linear planar delayed differential system x(center dot)(t) = Ax(t) + Bx(t-tau), where t >= 0, tau > 0 is a constant delay and A, Bare 2 x 2 constant matrices. Assuming that the system is weakly delayed, its general solution is constructed utilizing the Laplace transform. All the cases are specified of the solutions merging. Moreover, ordinary differential systems are considered such that general solutions of both delayed and non-delayed systems coincide when a transient interval is passed. Initial data for the relevant non-delayed systems are used such that these define the same solution as the corresponding initial data to the delayed system. An analysis of previous findings is given with two illustrative examples considered. Some open problems are suggested as well.

Keywords

Linear delayed system; Planar system; Weak delay; Single delay; Equivalent non-delayed system; Constant coefficients

Key words in English

Linear delayed system; Planar system; Weak delay; Single delay; Equivalent non-delayed system; Constant coefficients

Authors

DEREVIANKO, A.; DIBLÍK, J.

Released

01.12.2025

Periodical

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Volume

552

Number

1

State

United States of America

Pages from

1

Pages to

29

Pages count

29

URL

https://www.sciencedirect.com/science/article/pii/S0022247X25005219?via%3Dihub

BibTex

@article{BUT198231,
  author="Anna {Derevianko} and Josef {Diblík}",
  title="Planar linear differential weakly delayed systems with constant matrices and equivalent ordinary differential systems",
  journal="JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS",
  year="2025",
  volume="552",
  number="1",
  pages="1--29",
  doi="10.1016/j.jmaa.2025.129740",
  issn="0022-247X",
  url="https://www.sciencedirect.com/science/article/pii/S0022247X25005219?via%3Dihub"
}