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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Main Authors: Guangfeng Dong, Jaume Llibre
Format: Article
Language:English
Published: Vilnius University Press 2024-12-01
Series:Nonlinear Analysis
Subjects:
Online Access:https://www.zurnalai.vu.lt/nonlinear-analysis/article/view/37850
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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.
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