In this talk I report some of our recent findings concerning the emergence of synchronization transition in higher-order Kuramoto dynamics on simplicial complexes. 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. Most of the existing dynamical models defined on simplicial complexes make the strong assumption that the dynamics resides exclusively on the nodes, which is a strong simplification. 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 explore conditions in which higher-order Kuramoto dynamics can lead to an explosive synchronization transition which is achieved using an adaptive coupling dependent on the solenoidal and the irrotational component of the dynamics.
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