General solutions of weakly delayed discrete systems in 3D

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26110%2F26%3A0199321" target="_blank" >RIV/00216305:26110/26:0199321 - isvavai.cz</a>
Result on the web
<a href="https://www.degruyterbrill.com/document/doi/10.1515/anona-2025-0121/html" target="_blank" >https://www.degruyterbrill.com/document/doi/10.1515/anona-2025-0121/html</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/anona-2025-0121" target="_blank" >10.1515/anona-2025-0121</a>

Result language
angličtina
Original language name
General solutions of weakly delayed discrete systems in 3D
Original language description
Discrete systems x ( k + 1 ) = A x ( k ) + B x ( k - m ) xleft(k+1)=Axleft(k)+Bxleft(k-m) , k = 0 , 1 , & mldr; k=0,1,ldots hspace{0.33em} are analyzed, where m m is a fixed positive integer, A A , B B are constant 3 by 3 matrices and x : { - m , - m + 1 , & mldr; } -> R 3 x:left{-m,-m+1,ldots right}to {{mathbb{R}}}{3} . Assuming that the system is weakly delayed, its general solution is constructed for every case of the Jordan form of the matrix A A . It is shown that, for k >= 3 m kge 3m or for k >= 2 m kge 2m , these formulas reduce to simple forms depending on only the three independent parameters generated by the initial values. Formulas connecting these parameters with the initial ones are found. The results are illustrated by examples. Open problems for future research are discussed, and comparisons are given with the previous results.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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