Spatial Effects of Phase Dynamics on Oscillators Close to Bifurcation
The phase reduction approach has manifested its efficacy in investigating synchronization behaviors in limit-cycle oscillators. However, spatial distributions of the phase value on the limit cycle may lead to illusions of synchronizations for oscillators close to bifurcations. In this paper, we comp...
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MDPI AG
2023-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/11/2573 |
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| author | Yihan Wang Jinjie Zhu |
| author_facet | Yihan Wang Jinjie Zhu |
| author_sort | Yihan Wang |
| collection | DOAJ |
| description | The phase reduction approach has manifested its efficacy in investigating synchronization behaviors in limit-cycle oscillators. However, spatial distributions of the phase value on the limit cycle may lead to illusions of synchronizations for oscillators close to bifurcations. In this paper, we compared the phase sensitivity function in the spatial domain and time domain for oscillators close to saddle-node homoclinic (SNH) bifurcation, also known as saddle-node bifurcation on an invariant circle. It was found that the phase sensitivity function in the spatial domain can show the phase accumulation feature on the limit cycle, which can be ignored in the phase sensitivity function in the time domain. As an example, the synchronization distributions of uncoupled SNH oscillators driven by common and independent noises were investigated, where the space-dependent coupling function was considered on common noise. These results shed some light on the phase dynamics of oscillators close to bifurcations. |
| first_indexed | 2024-03-11T03:02:12Z |
| format | Article |
| id | doaj.art-fc05dfca672446c499d66048f3f536b1 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T03:02:12Z |
| publishDate | 2023-06-01 |
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| series | Mathematics |
| spelling | doaj.art-fc05dfca672446c499d66048f3f536b12023-11-18T08:13:52ZengMDPI AGMathematics2227-73902023-06-011111257310.3390/math11112573Spatial Effects of Phase Dynamics on Oscillators Close to BifurcationYihan Wang0Jinjie Zhu1School of Mathematics and Statistics, The University of Melbourne, Melbourne, VIC 3010, AustraliaState Key Laboratory of Mechanics and Control of Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, ChinaThe phase reduction approach has manifested its efficacy in investigating synchronization behaviors in limit-cycle oscillators. However, spatial distributions of the phase value on the limit cycle may lead to illusions of synchronizations for oscillators close to bifurcations. In this paper, we compared the phase sensitivity function in the spatial domain and time domain for oscillators close to saddle-node homoclinic (SNH) bifurcation, also known as saddle-node bifurcation on an invariant circle. It was found that the phase sensitivity function in the spatial domain can show the phase accumulation feature on the limit cycle, which can be ignored in the phase sensitivity function in the time domain. As an example, the synchronization distributions of uncoupled SNH oscillators driven by common and independent noises were investigated, where the space-dependent coupling function was considered on common noise. These results shed some light on the phase dynamics of oscillators close to bifurcations.https://www.mdpi.com/2227-7390/11/11/2573phase dynamicssaddle-node homoclinic bifurcationsynchronization |
| spellingShingle | Yihan Wang Jinjie Zhu Spatial Effects of Phase Dynamics on Oscillators Close to Bifurcation Mathematics phase dynamics saddle-node homoclinic bifurcation synchronization |
| title | Spatial Effects of Phase Dynamics on Oscillators Close to Bifurcation |
| title_full | Spatial Effects of Phase Dynamics on Oscillators Close to Bifurcation |
| title_fullStr | Spatial Effects of Phase Dynamics on Oscillators Close to Bifurcation |
| title_full_unstemmed | Spatial Effects of Phase Dynamics on Oscillators Close to Bifurcation |
| title_short | Spatial Effects of Phase Dynamics on Oscillators Close to Bifurcation |
| title_sort | spatial effects of phase dynamics on oscillators close to bifurcation |
| topic | phase dynamics saddle-node homoclinic bifurcation synchronization |
| url | https://www.mdpi.com/2227-7390/11/11/2573 |
| work_keys_str_mv | AT yihanwang spatialeffectsofphasedynamicsonoscillatorsclosetobifurcation AT jinjiezhu spatialeffectsofphasedynamicsonoscillatorsclosetobifurcation |