Explosive Higher-Order Kuramoto Dynamics on Simplicial Complexes
Ana P. Millán, Joaquı́n J. Torres, Ginestra Bianconi
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.
Topics & Concepts
Kuramoto modelDynamics (music)Order (exchange)Synchronization (alternating current)Conservative vector fieldSolenoidal vector fieldCoupling (piping)PhysicsStatistical physicsMathematicsComputer scienceTopology (electrical circuits)CombinatoricsCompressibilityVector fieldMechanicsMaterials scienceEconomicsFinanceMetallurgyAcousticsNonlinear Dynamics and Pattern FormationSlime Mold and Myxomycetes ResearchNeural dynamics and brain function