Low-Dimensional Reduction Theory for Populations of Globally Coupled Phase Oscillators with Multiharmonic Coupling: A Method Based on OPUC Theory
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866916070263095296 |
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| author | Tokunaga, Kai |
| author_facet | Tokunaga, Kai |
| contents | Low-dimensional reduction theories such as the Ott-Antonsen ansatz have played a crucial role in the study of populations of coupled oscillators. However, most of these theories apply only to models in which the interaction is described by a single harmonic component, limiting their use in more realistic oscillator models. Using the theory of orthogonal polynomials on the unit circle (OPUC), we develop a low-dimensional reduction theory for populations of globally coupled phase oscillators with multiharmonic coupling. We show theoretically and numerically that it is exact for uniformly rotating solutions and provides a good approximation for nonequilibrium solutions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_14611 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Low-Dimensional Reduction Theory for Populations of Globally Coupled Phase Oscillators with Multiharmonic Coupling: A Method Based on OPUC Theory Tokunaga, Kai Adaptation and Self-Organizing Systems Low-dimensional reduction theories such as the Ott-Antonsen ansatz have played a crucial role in the study of populations of coupled oscillators. However, most of these theories apply only to models in which the interaction is described by a single harmonic component, limiting their use in more realistic oscillator models. Using the theory of orthogonal polynomials on the unit circle (OPUC), we develop a low-dimensional reduction theory for populations of globally coupled phase oscillators with multiharmonic coupling. We show theoretically and numerically that it is exact for uniformly rotating solutions and provides a good approximation for nonequilibrium solutions. |
| title | Low-Dimensional Reduction Theory for Populations of Globally Coupled Phase Oscillators with Multiharmonic Coupling: A Method Based on OPUC Theory |
| topic | Adaptation and Self-Organizing Systems |
| url | https://arxiv.org/abs/2604.14611 |