Detail publikace

Explicit general solution of planar linear discrete systems with constant coefficients and weak delays

DIBLÍK, J. HALFAROVÁ, H.

Originální název

Explicit general solution of planar linear discrete systems with constant coefficients and weak delays

Typ

článek v časopise - ostatní, Jost

Jazyk

angličtina

Originální abstrakt

In this paper, planar linear discrete systems with constant coefficients and two delays $$ x(k+1)=Ax(k)+Bx(k-m)+Cx(k-n) $$ are considered where $k\in\bZ_0^{\infty}:=\{0,1,\dots,\infty\}$, $x\colon \bZ_0^{\infty}\to\mathbb{R}^2$, $m>n>0$ are fixed integers and $A=(a_{ij})$, $B=(b_{ij})$ and $C=(c_{ij})$ are constant $2\times 2$ matrices. It is assumed that the system considered system is one with weak delays. The characteristic equations of such systems are identical with those for the same systems but without delayed terms. In this case, after several steps, the space of solutions with a given starting dimension $2(m+1)$ is pasted into a space with a dimension less than the starting one. In a sense, this situation is analogous to one known in the theory of linear differential systems with constant coefficients and weak delays when the initially infinite dimensional space of solutions on the initial interval turns (after several steps) into a finite dimensional set of solutions. For every possible case, explicit general solutions are constructed and, finally, results on the dimensionality of the space of solutions are obtained.

Klíčová slova

Discrete equation, weak delays, explicit solution, dimension of the solutions space.

Autoři

DIBLÍK, J.; HALFAROVÁ, H.

Rok RIV

2013

Vydáno

6. 3. 2013

Nakladatel

Springer Nature

ISSN

1687-1847

Periodikum

Advances in Difference Equations

Ročník

2013

Číslo

1

Stát

Spojené státy americké

Strany od

1

Strany do

29

Strany počet

37

URL

Plný text v Digitální knihovně

BibTex

@article{BUT98366,
  author="Josef {Diblík} and Hana {Boháčková}",
  title="Explicit general solution of planar linear discrete systems with constant coefficients and weak delays",
  journal="Advances in Difference Equations",
  year="2013",
  volume="2013",
  number="1",
  pages="1--29",
  doi="10.1186/1687-1847-2013-50",
  issn="1687-1847",
  url="https://advancesindifferenceequations.springeropen.com/articles/10.1186/1687-1847-2013-50"
}