Periodic orbits for an autonomous version of the Duffing–Holmes oscillator
In the autonomous Duffing–Holmes oscillator, the existence of periodic orbits was detected numerically. Using the Hopf bifurcation theory, we prove analytically that such periodic orbits exist. We also provide the exact bifurcation value where the Hopf bifurcation takes place.
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2024-12-01
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| Series: | Nonlinear Analysis |
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| Online Access: | https://www.zurnalai.vu.lt/nonlinear-analysis/article/view/37850 |
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| _version_ | 1850191615603245056 |
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| author | Guangfeng Dong Jaume Llibre |
| author_facet | Guangfeng Dong Jaume Llibre |
| author_sort | Guangfeng Dong |
| collection | DOAJ |
| description |
In the autonomous Duffing–Holmes oscillator, the existence of periodic orbits was detected numerically. Using the Hopf bifurcation theory, we prove analytically that such periodic orbits exist. We also provide the exact bifurcation value where the Hopf bifurcation takes place.
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| format | Article |
| id | doaj-art-b47d4e3b29614de7a51e43bbccff521d |
| institution | OA Journals |
| issn | 1392-5113 2335-8963 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Nonlinear Analysis |
| spelling | doaj-art-b47d4e3b29614de7a51e43bbccff521d2025-08-20T02:14:51ZengVilnius University PressNonlinear Analysis1392-51132335-89632024-12-0129610.15388/namc.2024.29.37850Periodic orbits for an autonomous version of the Duffing–Holmes oscillatorGuangfeng Dong0Jaume Llibre1Jinan UniversityUniversitat Autònoma de Barcelona In the autonomous Duffing–Holmes oscillator, the existence of periodic orbits was detected numerically. Using the Hopf bifurcation theory, we prove analytically that such periodic orbits exist. We also provide the exact bifurcation value where the Hopf bifurcation takes place. https://www.zurnalai.vu.lt/nonlinear-analysis/article/view/37850Hopf bifurcationDuffing–Holmes oscillatorperiod orbit |
| spellingShingle | Guangfeng Dong Jaume Llibre Periodic orbits for an autonomous version of the Duffing–Holmes oscillator Nonlinear Analysis Hopf bifurcation Duffing–Holmes oscillator period orbit |
| title | Periodic orbits for an autonomous version of the Duffing–Holmes oscillator |
| title_full | Periodic orbits for an autonomous version of the Duffing–Holmes oscillator |
| title_fullStr | Periodic orbits for an autonomous version of the Duffing–Holmes oscillator |
| title_full_unstemmed | Periodic orbits for an autonomous version of the Duffing–Holmes oscillator |
| title_short | Periodic orbits for an autonomous version of the Duffing–Holmes oscillator |
| title_sort | periodic orbits for an autonomous version of the duffing holmes oscillator |
| topic | Hopf bifurcation Duffing–Holmes oscillator period orbit |
| url | https://www.zurnalai.vu.lt/nonlinear-analysis/article/view/37850 |
| work_keys_str_mv | AT guangfengdong periodicorbitsforanautonomousversionoftheduffingholmesoscillator AT jaumellibre periodicorbitsforanautonomousversionoftheduffingholmesoscillator |