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

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26110%2F13%3APU102874" target="_blank" >RIV/00216305:26110/13:PU102874 - isvavai.cz</a>

Výsledek na webu

<a href="https://advancesindifferenceequations.springeropen.com/articles/10.1186/1687-1847-2013-50" target="_blank" >https://advancesindifferenceequations.springeropen.com/articles/10.1186/1687-1847-2013-50</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1186/1687-1847-2013-50" target="_blank" >10.1186/1687-1847-2013-50</a>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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 $kinbZ_0^{infty}:={0,1,dots,infty}$, $xcolon bZ_0^{infty}tomathbb{R}^2$, $m>n>0$ are fixed integers and $A=(a_{ij})$, $B=(b_{ij})$ and $C=(c_{ij})$ are constant $2times 2$ 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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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 $kinbZ_0^{infty}:={0,1,dots,infty}$, $xcolon bZ_0^{infty}tomathbb{R}^2$, $m>n>0$ are fixed integers and $A=(a_{ij})$, $B=(b_{ij})$ and $C=(c_{ij})$ are constant $2times 2$ 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.

Druh

J_ost - Ostatní články v recenzovaných periodicích

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/ED2.1.00%2F03.0097" target="_blank" >ED2.1.00/03.0097: AdMaS - Pokročilé stavební materiály, konstrukce a technologie</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2013

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Advances in Difference Equations

ISSN

1687-1839

e-ISSN

1687-1847

Svazek periodika

2013

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

37

Strana od-do

1-29

Kód UT WoS článku

—

EID výsledku v databázi Scopus

—