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

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