Explosive higher-order Kuramoto dynamics on simplicial complexes
Adaptation and Self-Organizing Systems2020-06-02v3Disordered Systems and Neural NetworksStatistical MechanicsSocial and Information NetworksBiological PhysicsPhysics and Society
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.
@article{arxiv.1912.04405,
title = {Explosive higher-order Kuramoto dynamics on simplicial complexes},
author = {Ana P. Millán and Joaquín J. Torres and Ginestra Bianconi},
journal= {arXiv preprint arXiv:1912.04405},
year = {2020}
}