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Enlarged Kuramoto model: Secondary instability and transition to collective chaos

Abstract: 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 (nonpairwise) interactions, which induce strikingly complex phenomenology at certain parameter values. As the coupling is increased, a secondary instability renders the synchronized state unstable, and subsequent bifurcations lead to collective chaos. An efficient numerical study of the thermodynamic limit, valid for Gaussian heterogeneity, is carried out by means of a Fourier-Hermite decomposition of the oscillator density.

 Authorship: León I., Pazó D.,

 Fuente: Physical Review E, 2022, 105, L042201

 Publisher: American Physical Society

 Year of publication: 2022

 No. of pages: 6

 Publication type: Article

 DOI: 10.1103/PhysRevE.105.L042201

 ISSN: 1539-3755,1550-2376,2470-0045,2470-0053

 Spanish project: FIS2016-74957-P

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