Dynamics of large oscillator populations with random interactions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909261302333440 |
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| author | Pikovsky, Arkady Smirnov, Lev A. |
| author_facet | Pikovsky, Arkady Smirnov, Lev A. |
| contents | We explore large populations of phase oscillators interacting via random coupling functions. Two types of coupling terms, the Kuramoto-Daido coupling and the Winfree coupling, are considered. Under the assumption of statistical independence of the phases and the couplings, we derive reduced averaged equations with effective non-random coupling terms. As a particular example, we study interactions that have the same shape but possess random coupling strengths and random phase shifts. While randomness in coupling strengths just renormalizes the interaction, a distribution of the phase shifts in coupling reshapes the coupling function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06193 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamics of large oscillator populations with random interactions Pikovsky, Arkady Smirnov, Lev A. Adaptation and Self-Organizing Systems Disordered Systems and Neural Networks We explore large populations of phase oscillators interacting via random coupling functions. Two types of coupling terms, the Kuramoto-Daido coupling and the Winfree coupling, are considered. Under the assumption of statistical independence of the phases and the couplings, we derive reduced averaged equations with effective non-random coupling terms. As a particular example, we study interactions that have the same shape but possess random coupling strengths and random phase shifts. While randomness in coupling strengths just renormalizes the interaction, a distribution of the phase shifts in coupling reshapes the coupling function. |
| title | Dynamics of large oscillator populations with random interactions |
| topic | Adaptation and Self-Organizing Systems Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2404.06193 |