Stability of a Functional Differential System with a Finite Number of Delays
The paper is devoted to the study of asymptotic properties of a real two-dimensional differential system with unbounded nonconstant delays. The sufficient conditions for the stability and asymptotic stability of solutions are given. Used methods are based on the transformation of the considered real...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/853134 |
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| _version_ | 1850234907121418240 |
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| author | Josef Rebenda Zdeněk Šmarda |
| author_facet | Josef Rebenda Zdeněk Šmarda |
| author_sort | Josef Rebenda |
| collection | DOAJ |
| description | The paper is devoted to the study of asymptotic properties of a real two-dimensional differential system with unbounded nonconstant delays. The sufficient conditions for the stability and asymptotic stability of solutions are given. Used methods are based on the transformation of the considered real system to one equation with complex-valued coefficients. Asymptotic properties are studied by means of Lyapunov-Krasovskii functional. The results generalize some previous ones, where the asymptotic properties for two-dimensional systems with one or more constant delays or one nonconstant delay were studied. |
| format | Article |
| id | doaj-art-1816a697d98f4d6986b146b24a992bb8 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-1816a697d98f4d6986b146b24a992bb82025-08-20T02:02:29ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/853134853134Stability of a Functional Differential System with a Finite Number of DelaysJosef Rebenda0Zdeněk Šmarda1CEITEC BUT, Brno University of Technology, Technicka 3058/10, 61600 Brno, Czech RepublicCEITEC BUT, Brno University of Technology, Technicka 3058/10, 61600 Brno, Czech RepublicThe paper is devoted to the study of asymptotic properties of a real two-dimensional differential system with unbounded nonconstant delays. The sufficient conditions for the stability and asymptotic stability of solutions are given. Used methods are based on the transformation of the considered real system to one equation with complex-valued coefficients. Asymptotic properties are studied by means of Lyapunov-Krasovskii functional. The results generalize some previous ones, where the asymptotic properties for two-dimensional systems with one or more constant delays or one nonconstant delay were studied.http://dx.doi.org/10.1155/2013/853134 |
| spellingShingle | Josef Rebenda Zdeněk Šmarda Stability of a Functional Differential System with a Finite Number of Delays Abstract and Applied Analysis |
| title | Stability of a Functional Differential System with a Finite Number of Delays |
| title_full | Stability of a Functional Differential System with a Finite Number of Delays |
| title_fullStr | Stability of a Functional Differential System with a Finite Number of Delays |
| title_full_unstemmed | Stability of a Functional Differential System with a Finite Number of Delays |
| title_short | Stability of a Functional Differential System with a Finite Number of Delays |
| title_sort | stability of a functional differential system with a finite number of delays |
| url | http://dx.doi.org/10.1155/2013/853134 |
| work_keys_str_mv | AT josefrebenda stabilityofafunctionaldifferentialsystemwithafinitenumberofdelays AT zdeneksmarda stabilityofafunctionaldifferentialsystemwithafinitenumberofdelays |