On the uniqueness of limit cycles for generalized Liénard systems
In this article, the general Liénard system dxdt=ϕ(y)−F(x),dydt=−g(x)\left\{\begin{array}{l}\frac{{\rm{d}}x}{{\rm{d}}t}=\phi (y)-F\left(x),\\ \frac{{\rm{d}}y}{{\rm{d}}t}=-g\left(x)\end{array}\right. is studied. By using the Filippov transformation, combined with the careful estimation of divergence...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2023-02-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2022-0558 |
| _version_ | 1811159369581068288 |
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| author | Zhou Hui Yuan Yueding |
| author_facet | Zhou Hui Yuan Yueding |
| author_sort | Zhou Hui |
| collection | DOAJ |
| description | In this article, the general Liénard system dxdt=ϕ(y)−F(x),dydt=−g(x)\left\{\begin{array}{l}\frac{{\rm{d}}x}{{\rm{d}}t}=\phi (y)-F\left(x),\\ \frac{{\rm{d}}y}{{\rm{d}}t}=-g\left(x)\end{array}\right. is studied. By using the Filippov transformation, combined with the careful estimation of divergence along the closed orbit, we prove the sufficient conditions for the uniqueness of limit cycles in this system. Our results extend almost all the related existing studies on the Liénard system. |
| first_indexed | 2024-04-10T05:41:02Z |
| format | Article |
| id | doaj.art-697ed851730740529add6413fc277ec9 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-04-10T05:41:02Z |
| publishDate | 2023-02-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-697ed851730740529add6413fc277ec92023-03-06T10:26:16ZengDe GruyterOpen Mathematics2391-54552023-02-0121150051510.1515/math-2022-0558On the uniqueness of limit cycles for generalized Liénard systemsZhou Hui0Yuan Yueding1School of Mathematics and Computer Sciences, Yichun University, Yichun, Jiangxi 336000, P. R. ChinaSchool of Mathematics and Statistics, Hunan University of Finance and Economics, Changsha, Hunan 410205, P. R. ChinaIn this article, the general Liénard system dxdt=ϕ(y)−F(x),dydt=−g(x)\left\{\begin{array}{l}\frac{{\rm{d}}x}{{\rm{d}}t}=\phi (y)-F\left(x),\\ \frac{{\rm{d}}y}{{\rm{d}}t}=-g\left(x)\end{array}\right. is studied. By using the Filippov transformation, combined with the careful estimation of divergence along the closed orbit, we prove the sufficient conditions for the uniqueness of limit cycles in this system. Our results extend almost all the related existing studies on the Liénard system.https://doi.org/10.1515/math-2022-0558generalized liénard systemlimit cyclesuniqueness34a2534c0734c0534c25 |
| spellingShingle | Zhou Hui Yuan Yueding On the uniqueness of limit cycles for generalized Liénard systems Open Mathematics generalized liénard system limit cycles uniqueness 34a25 34c07 34c05 34c25 |
| title | On the uniqueness of limit cycles for generalized Liénard systems |
| title_full | On the uniqueness of limit cycles for generalized Liénard systems |
| title_fullStr | On the uniqueness of limit cycles for generalized Liénard systems |
| title_full_unstemmed | On the uniqueness of limit cycles for generalized Liénard systems |
| title_short | On the uniqueness of limit cycles for generalized Liénard systems |
| title_sort | on the uniqueness of limit cycles for generalized lienard systems |
| topic | generalized liénard system limit cycles uniqueness 34a25 34c07 34c05 34c25 |
| url | https://doi.org/10.1515/math-2022-0558 |
| work_keys_str_mv | AT zhouhui ontheuniquenessoflimitcyclesforgeneralizedlienardsystems AT yuanyueding ontheuniquenessoflimitcyclesforgeneralizedlienardsystems |