A stochastic approximation for the finite-size Kuramoto-Sakaguchi model
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866911873445658624 |
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| author | Yue, Wenqi Gottwald, Georg A. |
| author_facet | Yue, Wenqi Gottwald, Georg A. |
| contents | We perform a stochastic model reduction of the Kuramoto-Sakaguchi model for finitely many coupled phase oscillators with phase frustration. Whereas in the thermodynamic limit coupled oscillators exhibit stationary states and a constant order parameter, finite-size networks exhibit persistent temporal fluctuations of the order parameter. These fluctuations are caused by the interaction of the synchronized oscillators with the non-entrained oscillators. We present numerical results suggesting that the collective effect of the non-entrained oscillators on the synchronized cluster can be approximated by a Gaussian process. This allows for an effective closed evolution equation for the synchronized oscillators driven by a Gaussian process which we approximate by a two-dimensional Ornstein-Uhlenbeck process. Our reduction reproduces the stochastic fluctuations of the order parameter and leads to a simple stochastic differential equation for the order parameter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_20048 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A stochastic approximation for the finite-size Kuramoto-Sakaguchi model Yue, Wenqi Gottwald, Georg A. Adaptation and Self-Organizing Systems Dynamical Systems We perform a stochastic model reduction of the Kuramoto-Sakaguchi model for finitely many coupled phase oscillators with phase frustration. Whereas in the thermodynamic limit coupled oscillators exhibit stationary states and a constant order parameter, finite-size networks exhibit persistent temporal fluctuations of the order parameter. These fluctuations are caused by the interaction of the synchronized oscillators with the non-entrained oscillators. We present numerical results suggesting that the collective effect of the non-entrained oscillators on the synchronized cluster can be approximated by a Gaussian process. This allows for an effective closed evolution equation for the synchronized oscillators driven by a Gaussian process which we approximate by a two-dimensional Ornstein-Uhlenbeck process. Our reduction reproduces the stochastic fluctuations of the order parameter and leads to a simple stochastic differential equation for the order parameter. |
| title | A stochastic approximation for the finite-size Kuramoto-Sakaguchi model |
| topic | Adaptation and Self-Organizing Systems Dynamical Systems |
| url | https://arxiv.org/abs/2310.20048 |