General solutions of weakly delayed discrete systems in 3D

Simple item page
dc.contributor.authorDiblík, Josefcs
dc.contributor.authorBoháčková, Hanacs
dc.contributor.authorRůžičková, Miroslavacs
dc.contributor.authorŠafařík, Jancs
dc.coverage.issue1cs
dc.coverage.volume14cs
dc.date.accessioned2025-11-19T12:34:59Z
dc.date.available2025-11-19T12:34:59Z
dc.date.issued2025-10-24cs
dc.description.abstractDiscrete systems x ( k + 1 ) = A x ( k ) + B x ( k - m ) x\left(k+1)=Ax\left(k)+Bx\left(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 k\ge 3m or for k >= 2 m k\ge 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.en
dc.description.abstractDiscrete systems x ( k + 1 ) = A x ( k ) + B x ( k - m ) x\left(k+1)=Ax\left(k)+Bx\left(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 k\ge 3m or for k >= 2 m k\ge 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.en
dc.formattextcs
dc.format.extent1-49cs
dc.format.mimetypeapplication/pdfcs
dc.identifier.citationAdvances in Nonlinear Analysis. 2025, vol. 14, issue 1, p. 1-49.en
dc.identifier.doi10.1515/anona-2025-0121cs
dc.identifier.issn2191-9496cs
dc.identifier.orcid0000-0001-5009-316Xcs
dc.identifier.orcid0000-0002-1244-2733cs
dc.identifier.orcid0000-0001-8784-3382cs
dc.identifier.other199321cs
dc.identifier.researcheridD-3530-2014cs
dc.identifier.researcheridM-3203-2018cs
dc.identifier.scopus6701633618cs
dc.identifier.scopus57194683546cs
dc.identifier.urihttps://hdl.handle.net/11012/255627
dc.language.isoencs
dc.relation.ispartofAdvances in Nonlinear Analysiscs
dc.relation.urihttps://www.degruyterbrill.com/document/doi/10.1515/anona-2025-0121/htmlcs
dc.rightsCreative Commons Attribution 4.0 Internationalcs
dc.rights.accessopenAccesscs
dc.rights.sherpahttp://www.sherpa.ac.uk/romeo/issn/2191-9496/cs
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/cs
dc.subjectgeneral solutiondiscrete systemdelayweakly delayed systemindependent initial valuesen
dc.subjectgeneral solutiondiscrete systemdelayweakly delayed systemindependent initial values
dc.titleGeneral solutions of weakly delayed discrete systems in 3Den
dc.title.alternativeGeneral solutions of weakly delayed discrete systems in 3Den
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
sync.item.dbidVAV-199321en
sync.item.dbtypeVAVen
sync.item.insts2025.11.19 13:33:40en
sync.item.modts2025.11.18 11:32:58en
thesis.grantorVysoké učení technické v Brně. Fakulta stavební. Ústav matematiky a deskriptivní geometriecs
thesis.grantorVysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií. Ústav matematikycs
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
10.1515_anona20250121.pdf
Size:
4.95 MB
Format:
Adobe Portable Document Format
Description:
file 10.1515_anona20250121.pdf
Download
Collections
Ústav matematiky a deskriptivní geometrie
Ústav matematiky