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arXiv · 1912.04405

Explosive higher-order Kuramoto dynamics on simplicial complexes

Ana P. Millán·Joaquín J. Torres·Ginestra Bianconi
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Abstract

The higher-order interactions of complex systems, such as the brain are captured by their simplicial complex structure and have a significant effect on dynamics. However, the existing dynamical models defined on simplicial complexes make the strong assumption that the dynamics resides exclusively on the nodes. Here we formulate the higher-order Kuramoto model which describes the interactions between oscillators placed not only on nodes but also on links, triangles, and so on. We show that higher-order Kuramoto dynamics can lead to an explosive synchronization transition by using an adaptive coupling dependent on the solenoidal and the irrotational component of the dynamics.

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Ana P. Millán, Joaquín J. Torres, Ginestra Bianconi. 2019-12-09. Explosive higher-order Kuramoto dynamics on simplicial complexes. https://doi.org/10.1103/physrevlett.124.218301

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