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arXiv · 1902.01247

The effect of time-correlated noise on the Kuramoto model studied via the unified colored noise approximation

Claudio Maggi·Matteo Paoluzzi
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Abstract

Many natural and social phenomena are characterized by synchronization. The Kuramoto model, taking into account the basic ingredients for observing synchronized states, allows to study mathematically synchronization in a simplified but nontrivial picture. Here we study how a noise that is correlated on a finite time-scale $\tau$ impacts the ability of the Kuramoto model to achieve synchronization. We develop an approximated theory that allows to compute the critical coupling constant $k_c$ as a function of the correlation time $\tau$. We obtain that that $k_c(\tau)$ decreases as $\tau$ increases indicating that time-correlated noise promotes synchronization. Moreover, we show that theory describes qualitatively well the degree of synchronization near $k_c$ obtained numerically. Finally, we show that, independently on the value of $\tau$, the curves of the order parameter versus $k$ scale on the same master curve even at values of $k$ very far from $k_c$.

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Claudio Maggi, Matteo Paoluzzi. 2019-02-04. The effect of time-correlated noise on the Kuramoto model studied via the unified colored noise approximation. https://arxiv.org/abs/1902.01247

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