Emergent collective behaviors of stochastic kuramoto oscillators

Seung-Yeal Ha, Dongnam Ko, Chanho Min, Xiongtao Zhang. Emergent collective behaviors of stochastic kuramoto oscillators. Vol. 25, No. 3, pp. 1059-1081 (2020) DOI: 10.3934/dcdsb.2019208

Abstract. 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.

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