Explosive higher-order Kuramoto dynamics on simplicial complexes
arXiv:1912.04405 · doi:10.1103/PhysRevLett.124.218301
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.
(5 pages, 3 figures) + SM (12 pages, 10 figures)