A center manifold reduction of the Kuramoto-Daido model with a phase-lag

Hayato Chiba

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arXiv · 1609.04126

A center manifold reduction of the Kuramoto-Daido model with a phase-lag

Hayato Chiba

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Abstract

A bifurcation from the incoherent state to the partially synchronized state of the Kuramoto-Daido model with the coupling function $f(\theta ) = \sin (\theta +\alpha _1) + h\sin 2(\theta +\alpha _2)$ is investigated based on the generalized spectral theory and the center manifold reduction. The dynamical system of the order parameter on a center manifold is derived under the assumption that there exists a center manifold on the dual space of a certain test function space. It is shown that the incoherent state loses the stability at a critical coupling strength $K=K_c$, and a stable rotating partially synchronized state appears for $K>K_c$. The velocity of the rotating state is different from the average of natural frequencies of oscillators when $\alpha _1 \neq 0$.

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Hayato Chiba. 2016-09-14. A center manifold reduction of the Kuramoto-Daido model with a phase-lag. https://arxiv.org/abs/1609.04126

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