Emergent dynamics of the inertial Kuramoto model with frustration on a locally coupled graph

Tingting Zhu; Xiongtao Zhang

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arXiv · 2404.18488

Emergent dynamics of the inertial Kuramoto model with frustration on a locally coupled graph

Tingting Zhu·Xiongtao Zhang

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Abstract

We study the synchronized behavior of the inertial Kuramoto oscillators with frustration effect under a symmetric and connected network. Due to the lack of second-order gradient flow structure and singularity of second-order derivative of diameter, we shift to construct convex combinations of oscillators and related new energy functions that can control the phase and frequency diameters. Under sufficient frameworks on initial data and system parameters, we derive first-order dissipative differential inequalities of constructed energy functions. This eventually gives rise to the emergence of frequency synchronization exponentially fast.

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Tingting Zhu, Xiongtao Zhang. 2024-04-29. Emergent dynamics of the inertial Kuramoto model with frustration on a locally coupled graph. https://arxiv.org/abs/2404.18488

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