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Emergent collective behaviors of stochastic kuramoto oscillators

  • * Corresponding author: Dongnam Ko

    * Corresponding author: Dongnam Ko 

The work of S.-Y. Ha is supported by the NRF grant (2017R1A2B2001864). The work of D. Ko is supported by the European Research Council under the European Union's Horizon 2020 research and innovation programme (ERC-2015-AdG-694126-DyCon) and partially supported by CNCS-UEFISCDI Grant No. PN-III-P4-ID-PCE-2016-0035. The work of X. Zhang is supported by the National Natural Science Foundation of China (Grant No. 11801194)

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  • We study the collective dynamics of Kuramoto ensemble under uncertain coupling strength. For a finite ensemble, we can model the dynamics of the Kuramoto ensemble by the stochastic Kuramoto system with multiplicative noise. In contrast, for an infinite ensemble, the dynamics is effectively described by the Kuramoto-Sakaguchi-Fokker-Planck(KS-FP) equation with state dependent degenerate diffusion. We present emergent synchronization estimates for the stochastic and kinetic models, which yield the stability of the phase-locked state for identical Kuramoto ensemble with the same natural frequencies. We also provide a brief explanation on the mean-field limit between two models.

    Mathematics Subject Classification: Primary: 92B25, 93E15; Secondary: 70K20.


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