Detail publikačního výsledku

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

DEREVIANKO, A.; DIBLÍK, J.

Originální název

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

Anglický název

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

Druh

Článek WoS

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

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

Klíčová slova v angličtině

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

Autoři

DEREVIANKO, A.; DIBLÍK, J.

Vydáno

01.12.2025

Periodikum

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Svazek

552

Číslo

1

Stát

Spojené státy americké

Strany od

1

Strany do

29

Strany počet

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"
}