# Enlarged Kuramoto model: Secondary instability and transition to collective chaos.

@article{Leon2022EnlargedKM, title={Enlarged Kuramoto model: Secondary instability and transition to collective chaos.}, author={Iv'an Le'on and Diego Paz'o}, journal={Physical review. E}, year={2022}, volume={105 4}, pages={ L042201 } }

The emergence of collective synchrony from an incoherent state is a phenomenon essentially described by the Kuramoto model. This canonical model was derived perturbatively, by applying phase reduction to an ensemble of heterogeneous, globally coupled Stuart-Landau oscillators. This derivation neglects nonlinearities in the coupling constant. We show here that a comprehensive analysis requires extending the Kuramoto model up to quadratic order. This "enlarged Kuramoto model" comprises three-body…

## One Citation

Efficient moment-based approach to the simulation of infinitely many heterogeneous phase oscillators

- Mathematics
- 2022

The dynamics of ensembles of phase oscillators are usually described considering their inﬁnite-size limit. In practice, however, this limit is fully accessible only if the Ott-Antonsen theory can be…

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