تقرير
A stochastic approximation for the finite-size Kuramoto-Sakaguchi model
| العنوان: | A stochastic approximation for the finite-size Kuramoto-Sakaguchi model |
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| المؤلفون: | Yue, Wenqi, Gottwald, Georg A. |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics Nonlinear Sciences |
| مصطلحات موضوعية: | Nonlinear Sciences - Adaptation and Self-Organizing Systems, Mathematics - Dynamical Systems |
| الوصف: | 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. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2310.20048 |
| رقم الأكسشن: | edsarx.2310.20048 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |