Detail publikačního výsledku

Asymptotic properties of delayed matrix exponential function via Lambert function

DIBLÍK, J.; SVOBODA, Z.

Originální název

Asymptotic properties of delayed matrix exponential function via Lambert function

Anglický název

Asymptotic properties of delayed matrix exponential function via Lambert function

Druh

Článek WoS

Originální abstrakt

In the case of first-order linear systems with single constant delay and with constant matrix, the application of the well-known step by step method (when ordinary diffrential equations with delay are solved) has recently been formalized using a special type matrix, called delayed matrix exponential. In the paper, the asymptotic properties of delayed matrix exponential are studied for and it is, e.g., proved that the sequence of values of a delayed matrix exponential at nodes is approximately represented by a geometric progression. A constant matrix has been found such that its matrix exponential is the quotient factor that depends on the principal branch of the Lambert function. Applications of the results obtained are given as well.

Anglický abstrakt

In the case of first-order linear systems with single constant delay and with constant matrix, the application of the well-known step by step method (when ordinary diffrential equations with delay are solved) has recently been formalized using a special type matrix, called delayed matrix exponential. In the paper, the asymptotic properties of delayed matrix exponential are studied for and it is, e.g., proved that the sequence of values of a delayed matrix exponential at nodes is approximately represented by a geometric progression. A constant matrix has been found such that its matrix exponential is the quotient factor that depends on the principal branch of the Lambert function. Applications of the results obtained are given as well.

Klíčová slova

Lambert function, delayed matrix exponential, asymptotic behavior, principal part, instability.

Klíčová slova v angličtině

Lambert function, delayed matrix exponential, asymptotic behavior, principal part, instability.

Autoři

DIBLÍK, J.; SVOBODA, Z.

Rok RIV

2019

Vydáno

15.01.2018

Nakladatel

Americal Institute of Mathematical Sciences

ISSN

1553-524X

Periodikum

Discrete and continuous dynamical systems - series B

Svazek

72

Číslo

10

Stát

Spojené státy americké

Strany od

123

Strany do

144

Strany počet

22

URL

http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=14696

BibTex

@article{BUT150426,
  author="Josef {Diblík} and Zdeněk {Svoboda}",
  title="Asymptotic properties of delayed matrix exponential function via Lambert function",
  journal="Discrete and continuous dynamical systems - series B",
  year="2018",
  volume="72",
  number="10",
  pages="123--144",
  doi="10.3934/dcdsb.2018008",
  issn="1531-3492",
  url="http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=14696"
}