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arXiv · 1509.04244

Approximate solution for frequency synchronisation in a finite-size Kuramoto model

Chengwei Wang·Nicolas Rubido·Celso Grebogi·Murilo S. Baptista
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Abstract

Scientists have been considering the Kuramoto model to understand the mechanism behind the appearance of collective behaviour, such as frequency synchronisation (FS) as a paradigm, in real-world networks with a finite number of oscillators. A major current challenge is to obtain an analytical solution for the phase-angles. Here, we provide an approximate analytical solution for this problem by deriving a master solution for the finite-size Kuramoto model, without imposing any restriction on the distribution of the natural frequencies of the oscillators. The master solution embodies all particular solutions of the finite-size Kuramoto model for any frequency distribution and coupling strength larger than the critical one. Furthermore, we present a criterion to determine the stability of the FS solution. This allows one to analytically infer the relationship between the physical parameters and the stable behaviour of networks.

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Chengwei Wang, Nicolas Rubido, Celso Grebogi, Murilo S. Baptista. 2015-09-11. Approximate solution for frequency synchronisation in a finite-size Kuramoto model. https://arxiv.org/abs/1509.04244

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