From Delay to Inertia and Triadic Interactions: A Predictive Model for Time-Delayed Oscillator Networks
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917480245493760 |
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| author | Smirnov, L. A. Munyayev, V. O. Bolotov, M. I. Belykh, I. |
| author_facet | Smirnov, L. A. Munyayev, V. O. Bolotov, M. I. Belykh, I. |
| contents | Time-delayed oscillator networks underlie diverse biological and physical systems, yet standard first-order phase reductions fail to capture their high-dimensional collective dynamics. In this Letter, we develop a universal second-order predictive reduction for time-delayed Kuramoto-Daido networks that maps delayed one-dimensional phase dynamics to a delay-free network of two-dimensional rotators. Delay induces effective inertia and triadic interactions, yielding accurate predictions of nontrivial attractors and their collective-state statistics, including splay, cyclops, and chimera states. The reduction reveals a division of roles: inertia organizes higher-dimensional dynamics, whereas triadic terms are crucial for lower-dimensional patterns such as chimeras. Applicable to arbitrary topology, higher harmonics, and intrinsic-frequency heterogeneity, it provides a compact, parameter-explicit reduced model. The same framework also extends to time-delayed amplitude-phase oscillator networks, including swarmalators, yielding analogous reduced equations with emergent inertia and triadic higher-order couplings. This unified and readily deployable description enables systematic prediction and analysis of delay-controlled collective dynamics across oscillator networks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_10806 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From Delay to Inertia and Triadic Interactions: A Predictive Model for Time-Delayed Oscillator Networks Smirnov, L. A. Munyayev, V. O. Bolotov, M. I. Belykh, I. Pattern Formation and Solitons Time-delayed oscillator networks underlie diverse biological and physical systems, yet standard first-order phase reductions fail to capture their high-dimensional collective dynamics. In this Letter, we develop a universal second-order predictive reduction for time-delayed Kuramoto-Daido networks that maps delayed one-dimensional phase dynamics to a delay-free network of two-dimensional rotators. Delay induces effective inertia and triadic interactions, yielding accurate predictions of nontrivial attractors and their collective-state statistics, including splay, cyclops, and chimera states. The reduction reveals a division of roles: inertia organizes higher-dimensional dynamics, whereas triadic terms are crucial for lower-dimensional patterns such as chimeras. Applicable to arbitrary topology, higher harmonics, and intrinsic-frequency heterogeneity, it provides a compact, parameter-explicit reduced model. The same framework also extends to time-delayed amplitude-phase oscillator networks, including swarmalators, yielding analogous reduced equations with emergent inertia and triadic higher-order couplings. This unified and readily deployable description enables systematic prediction and analysis of delay-controlled collective dynamics across oscillator networks. |
| title | From Delay to Inertia and Triadic Interactions: A Predictive Model for Time-Delayed Oscillator Networks |
| topic | Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2512.10806 |