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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
Číslo
1
Stát
Spojené státy americké
Strany od
Strany do
29
Strany počet
37
URL
https://advancesindifferenceequations.springeropen.com/articles/10.1186/1687-1847-2013-50
Plný text v Digitální knihovně
http://hdl.handle.net/11012/137963
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" }