High-order phase reduction for coupled 2D oscillators
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909285398609920 |
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| author | Mau, Erik T. K. Rosenblum, Michael Pikovsky, Arkady |
| author_facet | Mau, Erik T. K. Rosenblum, Michael Pikovsky, Arkady |
| contents | Phase reduction is a general approach to describe coupled oscillatory units in terms of their phases, assuming that the amplitudes are enslaved. For such a reduction, the coupling should be small, but one also expects the reduction to be valid for finite coupling. This paper presents a general framework allowing us to obtain coupling terms in higher orders of the coupling parameter for generic two-dimensional oscillators and arbitrary coupling terms. The theory is illustrated with an accurate prediction of Arnold's tongue for the van der Pol oscillator exploiting higher-order phase reduction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_14711 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | High-order phase reduction for coupled 2D oscillators Mau, Erik T. K. Rosenblum, Michael Pikovsky, Arkady Chaotic Dynamics Phase reduction is a general approach to describe coupled oscillatory units in terms of their phases, assuming that the amplitudes are enslaved. For such a reduction, the coupling should be small, but one also expects the reduction to be valid for finite coupling. This paper presents a general framework allowing us to obtain coupling terms in higher orders of the coupling parameter for generic two-dimensional oscillators and arbitrary coupling terms. The theory is illustrated with an accurate prediction of Arnold's tongue for the van der Pol oscillator exploiting higher-order phase reduction. |
| title | High-order phase reduction for coupled 2D oscillators |
| topic | Chaotic Dynamics |
| url | https://arxiv.org/abs/2307.14711 |