Conditional Stability and Asymptotic Behavior of Solutions of Weakly Delayed Linear Discrete Systems in R2
Two-dimensional linear discrete systems x(k+1)=Ax(k)+∑l=1nBlxl(k-ml), k≥0, are analyzed, where m1,m2,…,mn are constant integer delays, 0<m1<m2<⋯<mn, A, B1,…,Bn are constant 2×2 matrices, A=(aij), Bl=(bijl), i,j=1,2, l=1,2,…,n, and x:{-mn,-mn+1,…}→R2. Under the assumption that the syst...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2017-01-01
|
| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2017/6028078 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832559817636446208 |
|---|---|
| author | Josef Diblík Hana Halfarová Jan Šafařík |
| author_facet | Josef Diblík Hana Halfarová Jan Šafařík |
| author_sort | Josef Diblík |
| collection | DOAJ |
| description | Two-dimensional linear discrete systems x(k+1)=Ax(k)+∑l=1nBlxl(k-ml), k≥0, are analyzed, where m1,m2,…,mn are constant integer delays, 0<m1<m2<⋯<mn, A, B1,…,Bn are constant 2×2 matrices, A=(aij), Bl=(bijl), i,j=1,2, l=1,2,…,n, and x:{-mn,-mn+1,…}→R2. Under the assumption that the system is weakly delayed, the asymptotic behavior of its solutions is studied and asymptotic formulas are derived. |
| format | Article |
| id | doaj-art-33a39a1c75fb40ac98362a2a70d25253 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-33a39a1c75fb40ac98362a2a70d252532025-02-03T01:29:06ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2017-01-01201710.1155/2017/60280786028078Conditional Stability and Asymptotic Behavior of Solutions of Weakly Delayed Linear Discrete Systems in R2Josef Diblík0Hana Halfarová1Jan Šafařík2Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Brno University of Technology, Brno, Czech RepublicDepartment of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Brno University of Technology, Brno, Czech RepublicDepartment of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Brno University of Technology, Brno, Czech RepublicTwo-dimensional linear discrete systems x(k+1)=Ax(k)+∑l=1nBlxl(k-ml), k≥0, are analyzed, where m1,m2,…,mn are constant integer delays, 0<m1<m2<⋯<mn, A, B1,…,Bn are constant 2×2 matrices, A=(aij), Bl=(bijl), i,j=1,2, l=1,2,…,n, and x:{-mn,-mn+1,…}→R2. Under the assumption that the system is weakly delayed, the asymptotic behavior of its solutions is studied and asymptotic formulas are derived.http://dx.doi.org/10.1155/2017/6028078 |
| spellingShingle | Josef Diblík Hana Halfarová Jan Šafařík Conditional Stability and Asymptotic Behavior of Solutions of Weakly Delayed Linear Discrete Systems in R2 Discrete Dynamics in Nature and Society |
| title | Conditional Stability and Asymptotic Behavior of Solutions of Weakly Delayed Linear Discrete Systems in R2 |
| title_full | Conditional Stability and Asymptotic Behavior of Solutions of Weakly Delayed Linear Discrete Systems in R2 |
| title_fullStr | Conditional Stability and Asymptotic Behavior of Solutions of Weakly Delayed Linear Discrete Systems in R2 |
| title_full_unstemmed | Conditional Stability and Asymptotic Behavior of Solutions of Weakly Delayed Linear Discrete Systems in R2 |
| title_short | Conditional Stability and Asymptotic Behavior of Solutions of Weakly Delayed Linear Discrete Systems in R2 |
| title_sort | conditional stability and asymptotic behavior of solutions of weakly delayed linear discrete systems in r2 |
| url | http://dx.doi.org/10.1155/2017/6028078 |
| work_keys_str_mv | AT josefdiblik conditionalstabilityandasymptoticbehaviorofsolutionsofweaklydelayedlineardiscretesystemsinr2 AT hanahalfarova conditionalstabilityandasymptoticbehaviorofsolutionsofweaklydelayedlineardiscretesystemsinr2 AT jansafarik conditionalstabilityandasymptoticbehaviorofsolutionsofweaklydelayedlineardiscretesystemsinr2 |