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arXiv · 1909.03358

Emergent behaviors of the discrete-time Kuramoto model for generic initial configuration

Xiongtao Zhang·Tingting Zhu
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Abstract

In this paper, we will study the emergent dynamics of the discrete Kuramoto model for generic initial data. This is an extension of the previous work S.-Y. Ha et al. (2019), in which the initial configurations are supposed to be within a half circle. More precisely, we will provide the theory of discrete gradient flow which can be applied to general Euler iteration scheme. Therefore, as a direct application, we conclude the emergence of synchronization of discrete Kuramoto model. Moreover, we obtain for small mesh size that, the synchronization will occur exponentially fast for initial data in A_1 (see definition in (4.1)).

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Xiongtao Zhang, Tingting Zhu. 2019-09-08. Emergent behaviors of the discrete-time Kuramoto model for generic initial configuration. https://arxiv.org/abs/1909.03358

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