{"title":"参数激励下三稳振荡器的爆裂模式","authors":"Yue Zhou, Wen-An Jiang, Jin-Chao Cui","doi":"10.1007/s12648-024-03310-4","DOIUrl":null,"url":null,"abstract":"<p>The motion of the tri-stable oscillator can be transferred between different equilibrium points to produce a large response, which is the desire of vibration energy harvesting technology. Therefore, the vibration of the tri-stable system has been a widespread concern. However, the mechanism of the system with parametric slow excitations has not been discovered. To study this issue, we treat a novel bursting pattern in a tri-stable oscillator under slow cosinoidal excitations. The complex dynamic behaviors of bursting oscillation under single and two frequencies are presented using the fast-slow analysis method, the one-parameter bifurcation diagrams are plotted, and the bifurcation patterns associated with independent loop and closed loop are observed. Furthermore, different types of bursting oscillations induced by subcritical pitchfork/fold bifurcations are presented, and jumping phenomena and hysteresis behaviors are displayed. Moreover, the stabilities of equilibrium of the independent and closed loop positions are checked by potential energy, and the transition of different equilibrium configurations is validated by introducing the transformed phase diagram. Finally, the attraction basin of each equilibrium point is estimated via cell mapping, and the multivalued response orbits are recognized.</p>","PeriodicalId":584,"journal":{"name":"Indian Journal of Physics","volume":null,"pages":null},"PeriodicalIF":1.6000,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Bursting patterns in a tri-stable oscillator under parametric excitations\",\"authors\":\"Yue Zhou, Wen-An Jiang, Jin-Chao Cui\",\"doi\":\"10.1007/s12648-024-03310-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The motion of the tri-stable oscillator can be transferred between different equilibrium points to produce a large response, which is the desire of vibration energy harvesting technology. Therefore, the vibration of the tri-stable system has been a widespread concern. However, the mechanism of the system with parametric slow excitations has not been discovered. To study this issue, we treat a novel bursting pattern in a tri-stable oscillator under slow cosinoidal excitations. The complex dynamic behaviors of bursting oscillation under single and two frequencies are presented using the fast-slow analysis method, the one-parameter bifurcation diagrams are plotted, and the bifurcation patterns associated with independent loop and closed loop are observed. Furthermore, different types of bursting oscillations induced by subcritical pitchfork/fold bifurcations are presented, and jumping phenomena and hysteresis behaviors are displayed. Moreover, the stabilities of equilibrium of the independent and closed loop positions are checked by potential energy, and the transition of different equilibrium configurations is validated by introducing the transformed phase diagram. Finally, the attraction basin of each equilibrium point is estimated via cell mapping, and the multivalued response orbits are recognized.</p>\",\"PeriodicalId\":584,\"journal\":{\"name\":\"Indian Journal of Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2024-07-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Indian Journal of Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1007/s12648-024-03310-4\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indian Journal of Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s12648-024-03310-4","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
Bursting patterns in a tri-stable oscillator under parametric excitations
The motion of the tri-stable oscillator can be transferred between different equilibrium points to produce a large response, which is the desire of vibration energy harvesting technology. Therefore, the vibration of the tri-stable system has been a widespread concern. However, the mechanism of the system with parametric slow excitations has not been discovered. To study this issue, we treat a novel bursting pattern in a tri-stable oscillator under slow cosinoidal excitations. The complex dynamic behaviors of bursting oscillation under single and two frequencies are presented using the fast-slow analysis method, the one-parameter bifurcation diagrams are plotted, and the bifurcation patterns associated with independent loop and closed loop are observed. Furthermore, different types of bursting oscillations induced by subcritical pitchfork/fold bifurcations are presented, and jumping phenomena and hysteresis behaviors are displayed. Moreover, the stabilities of equilibrium of the independent and closed loop positions are checked by potential energy, and the transition of different equilibrium configurations is validated by introducing the transformed phase diagram. Finally, the attraction basin of each equilibrium point is estimated via cell mapping, and the multivalued response orbits are recognized.
期刊介绍:
Indian Journal of Physics is a monthly research journal in English published by the Indian Association for the Cultivation of Sciences in collaboration with the Indian Physical Society. The journal publishes refereed papers covering current research in Physics in the following category: Astrophysics, Atmospheric and Space physics; Atomic & Molecular Physics; Biophysics; Condensed Matter & Materials Physics; General & Interdisciplinary Physics; Nonlinear dynamics & Complex Systems; Nuclear Physics; Optics and Spectroscopy; Particle Physics; Plasma Physics; Relativity & Cosmology; Statistical Physics.