Higher-order phase reduction for delay-coupled oscillators beyond the phase-shift approximation
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909880445566976 |
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| author | Bick, Christian Rink, Bob W. de Wolff, Babette A. J. |
| author_facet | Bick, Christian Rink, Bob W. de Wolff, Babette A. J. |
| contents | Network interactions between dynamical units are often subject to time delay. We develop a phase reduction method for delay-coupled oscillator networks. The method is based on rewriting the delay-differential equation as an ordinary differential equation coupled with a transport equation, expanding in the coupling strength, and solving the resulting equations order-by-order. This approach yields an approximation of the finite-dimensional phase dynamics to arbitrary order. While in the first-order approximation the time delay acts as a phase shift as expected, the higher-order phase reduction generally displays a less trivial dependence on the delay. In particular, exploiting second-order phase reduction, we prove the existence of a region of bistability in the synchronization dynamics of two delay-coupled Stuart-Landau oscillators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_27524 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher-order phase reduction for delay-coupled oscillators beyond the phase-shift approximation Bick, Christian Rink, Bob W. de Wolff, Babette A. J. Dynamical Systems Adaptation and Self-Organizing Systems Chaotic Dynamics Network interactions between dynamical units are often subject to time delay. We develop a phase reduction method for delay-coupled oscillator networks. The method is based on rewriting the delay-differential equation as an ordinary differential equation coupled with a transport equation, expanding in the coupling strength, and solving the resulting equations order-by-order. This approach yields an approximation of the finite-dimensional phase dynamics to arbitrary order. While in the first-order approximation the time delay acts as a phase shift as expected, the higher-order phase reduction generally displays a less trivial dependence on the delay. In particular, exploiting second-order phase reduction, we prove the existence of a region of bistability in the synchronization dynamics of two delay-coupled Stuart-Landau oscillators. |
| title | Higher-order phase reduction for delay-coupled oscillators beyond the phase-shift approximation |
| topic | Dynamical Systems Adaptation and Self-Organizing Systems Chaotic Dynamics |
| url | https://arxiv.org/abs/2510.27524 |