On Stability of Periodic Solutions of Lienard Type Equations
We use the Floquet theory to analyze the stability of periodic solutions of Lienard type equations under the asymptotic linear growth of restoring force in this paper. We find that the existence and the stability of periodic solutions are determined primarily by asymptotic behavior of damping term....
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2017/1805760 |
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| _version_ | 1849434730606362624 |
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| author | Zijian Yin Hongbin Chen |
| author_facet | Zijian Yin Hongbin Chen |
| author_sort | Zijian Yin |
| collection | DOAJ |
| description | We use the Floquet theory to analyze the stability of periodic solutions of Lienard type equations under the asymptotic linear growth of restoring force in this paper. We find that the existence and the stability of periodic solutions are determined primarily by asymptotic behavior of damping term. For special type of Lienard equation, the uniqueness and stability of periodic solutions are obtained. Furthermore, the sharp rate of exponential decay of the stable periodic solutions is determined under suitable conditions imposed on restoring force. |
| format | Article |
| id | doaj-art-e40c43da171e4801b5a74fa0316ffbef |
| 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-e40c43da171e4801b5a74fa0316ffbef2025-08-20T03:26:33ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2017-01-01201710.1155/2017/18057601805760On Stability of Periodic Solutions of Lienard Type EquationsZijian Yin0Hongbin Chen1School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, ChinaSchool of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, ChinaWe use the Floquet theory to analyze the stability of periodic solutions of Lienard type equations under the asymptotic linear growth of restoring force in this paper. We find that the existence and the stability of periodic solutions are determined primarily by asymptotic behavior of damping term. For special type of Lienard equation, the uniqueness and stability of periodic solutions are obtained. Furthermore, the sharp rate of exponential decay of the stable periodic solutions is determined under suitable conditions imposed on restoring force.http://dx.doi.org/10.1155/2017/1805760 |
| spellingShingle | Zijian Yin Hongbin Chen On Stability of Periodic Solutions of Lienard Type Equations Discrete Dynamics in Nature and Society |
| title | On Stability of Periodic Solutions of Lienard Type Equations |
| title_full | On Stability of Periodic Solutions of Lienard Type Equations |
| title_fullStr | On Stability of Periodic Solutions of Lienard Type Equations |
| title_full_unstemmed | On Stability of Periodic Solutions of Lienard Type Equations |
| title_short | On Stability of Periodic Solutions of Lienard Type Equations |
| title_sort | on stability of periodic solutions of lienard type equations |
| url | http://dx.doi.org/10.1155/2017/1805760 |
| work_keys_str_mv | AT zijianyin onstabilityofperiodicsolutionsoflienardtypeequations AT hongbinchen onstabilityofperiodicsolutionsoflienardtypeequations |