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arXiv · 2409.08736

Bifurcations in the Kuramoto model with external forcing and higher-order interactions

Guilherme S. Costa·Marcel Novaes·Marcus A. M. de Aguiar
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Abstract

Synchronization is an important phenomenon in a wide variety of systems comprising interacting oscillatory units, whether natural (like neurons, biochemical reactions, cardiac cells) or artificial (like metronomes, power grids, Josephson junctions). The Kuramoto model provides a simple description of these systems and has been useful in their mathematical exploration. Here we investigate this model combining two common features that have been observed in many systems: external periodic forcing and higher-order interactions among the elements. We show that the combination of these ingredients leads to a very rich bifurcation scenario that produces 11 different asymptotic states of the system, with competition between forced and spontaneous synchronization. We found, in particular, that saddle-node, Hopf and homoclinic manifolds are duplicated in regions of parameter space where the unforced system displays bi-stability.

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Guilherme S. Costa, Marcel Novaes, Marcus A. M. de Aguiar. 2024-09-13. Bifurcations in the Kuramoto model with external forcing and higher-order interactions. https://doi.org/10.1063/5.0239011

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