Finite-Time Attractivity for Diagonally Dominant Systems with Off-Diagonal Delays
We introduce a notion of attractivity for delay equations which are defined on bounded time intervals. Our main result shows that linear delay equations are finite-time attractive, provided that the delay is only in the coupling terms between different components, and the system is diagonally domina...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/210156 |
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| _version_ | 1850237230821408768 |
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| author | T. S. Doan S. Siegmund |
| author_facet | T. S. Doan S. Siegmund |
| author_sort | T. S. Doan |
| collection | DOAJ |
| description | We introduce a notion of attractivity for delay equations which are defined on bounded time intervals. Our main result shows that linear delay equations are finite-time attractive, provided that the delay is only in the coupling terms between different components, and the system is diagonally dominant. We apply this result to a nonlinear Lotka-Volterra system and show that the delay is harmless and does not destroy finite-time attractivity. |
| format | Article |
| id | doaj-art-00458fb5e89d4165ad07f7e38e72ebff |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-00458fb5e89d4165ad07f7e38e72ebff2025-08-20T02:01:47ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/210156210156Finite-Time Attractivity for Diagonally Dominant Systems with Off-Diagonal DelaysT. S. Doan0S. Siegmund1Department of Mathematics, Imperial College London, London SW7 2AZ, UKCenter for Dynamics, TU Dresden, 01062 Dresden, GermanyWe introduce a notion of attractivity for delay equations which are defined on bounded time intervals. Our main result shows that linear delay equations are finite-time attractive, provided that the delay is only in the coupling terms between different components, and the system is diagonally dominant. We apply this result to a nonlinear Lotka-Volterra system and show that the delay is harmless and does not destroy finite-time attractivity.http://dx.doi.org/10.1155/2012/210156 |
| spellingShingle | T. S. Doan S. Siegmund Finite-Time Attractivity for Diagonally Dominant Systems with Off-Diagonal Delays Abstract and Applied Analysis |
| title | Finite-Time Attractivity for Diagonally Dominant Systems with Off-Diagonal Delays |
| title_full | Finite-Time Attractivity for Diagonally Dominant Systems with Off-Diagonal Delays |
| title_fullStr | Finite-Time Attractivity for Diagonally Dominant Systems with Off-Diagonal Delays |
| title_full_unstemmed | Finite-Time Attractivity for Diagonally Dominant Systems with Off-Diagonal Delays |
| title_short | Finite-Time Attractivity for Diagonally Dominant Systems with Off-Diagonal Delays |
| title_sort | finite time attractivity for diagonally dominant systems with off diagonal delays |
| url | http://dx.doi.org/10.1155/2012/210156 |
| work_keys_str_mv | AT tsdoan finitetimeattractivityfordiagonallydominantsystemswithoffdiagonaldelays AT ssiegmund finitetimeattractivityfordiagonallydominantsystemswithoffdiagonaldelays |