The Asymptotic Behavior for a Class of Impulsive Delay Differential Equations
This paper is concerned with asymptotical behavior for a class of impulsive delay differential equations. The new criteria for determining attracting sets and attracting basin of the impulsive system are obtained by developing the properties of quasi-invariant sets. Examples and numerical simulation...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/494067 |
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| _version_ | 1832548955042349056 |
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| author | Zhichun Yang |
| author_facet | Zhichun Yang |
| author_sort | Zhichun Yang |
| collection | DOAJ |
| description | This paper is concerned with asymptotical behavior for a class of impulsive delay differential equations. The new criteria for determining attracting sets and attracting basin of the impulsive system are obtained by developing the properties of quasi-invariant sets. Examples and numerical simulations are given to illustrate the effectiveness of our results. In addition, we show that the impulsive effects may play a key role to these asymptotical properties even though the solutions of corresponding nonimpulsive systems are unbounded. |
| format | Article |
| id | doaj-art-73466ce065a34f17b255a684f0219dba |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-73466ce065a34f17b255a684f0219dba2025-02-03T06:12:37ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/494067494067The Asymptotic Behavior for a Class of Impulsive Delay Differential EquationsZhichun Yang0Department of Mathematics, Chongqing Normal University, Chongqing 400047, ChinaThis paper is concerned with asymptotical behavior for a class of impulsive delay differential equations. The new criteria for determining attracting sets and attracting basin of the impulsive system are obtained by developing the properties of quasi-invariant sets. Examples and numerical simulations are given to illustrate the effectiveness of our results. In addition, we show that the impulsive effects may play a key role to these asymptotical properties even though the solutions of corresponding nonimpulsive systems are unbounded.http://dx.doi.org/10.1155/2013/494067 |
| spellingShingle | Zhichun Yang The Asymptotic Behavior for a Class of Impulsive Delay Differential Equations Abstract and Applied Analysis |
| title | The Asymptotic Behavior for a Class of Impulsive Delay Differential Equations |
| title_full | The Asymptotic Behavior for a Class of Impulsive Delay Differential Equations |
| title_fullStr | The Asymptotic Behavior for a Class of Impulsive Delay Differential Equations |
| title_full_unstemmed | The Asymptotic Behavior for a Class of Impulsive Delay Differential Equations |
| title_short | The Asymptotic Behavior for a Class of Impulsive Delay Differential Equations |
| title_sort | asymptotic behavior for a class of impulsive delay differential equations |
| url | http://dx.doi.org/10.1155/2013/494067 |
| work_keys_str_mv | AT zhichunyang theasymptoticbehaviorforaclassofimpulsivedelaydifferentialequations AT zhichunyang asymptoticbehaviorforaclassofimpulsivedelaydifferentialequations |