## Synchronization of Kuramoto oscillators: inverse Taylor expansions.(English)Zbl 1462.34081

This comprehensive paper on Kuramoto model starts from the standard heterogeneous Kuramoto model $\displaystyle{\dot{\theta}_i = \omega_i - \sum_{j=1}^na_{ij}\sin(\theta_i-\theta_j)\ ,\ i=\overline{1,n}}$ and considers $$\{\mathbb{T}^n\}$$ to be its state space (due to the periodic nonlinearity sin). The essence of the approach is the analysis of the synchronization manifold and the convergence analysis using Taylor series expansions around it.

### MSC:

 34D06 Synchronization of solutions to ordinary differential equations 34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations 34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. 34D05 Asymptotic properties of solutions to ordinary differential equations

MATPOWER
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