Third order interactions shift the critical coupling in multidimensional Kuramoto models

Abstract

The study of higher order interactions in the dynamics of Kuramoto oscillators has been a topic of intense recent research. Arguments based on dimensional reduction using the Ott-Antonsen ansatz show that such interactions usually facilitate synchronization, giving rise to bi-stability and hysteresis. Here we show that three body interactions shift the critical coupling for synchronization towards higher values in all dimensions, except $D=2$, where a cancellation occurs. After the transition, three and four body interactions combine to facilitate synchronization. Similar to the 2-dimensional case, bi-stability and hysteresis develop for large enough higher order interactions. We show simulations in $D=3$ and $4$ to illustrate the dynamics.

arXiv comment15 pages, 4 figures. New analysis of bi-stability and hysteresis

References in corpus (17)

• Networks beyond pairwise interactions: structure and dynamics
• Higher-order organization of complex networks
• Simplicial models of social contagion
• Explosive Synchronization Transitions in Scale-free Networks
• Clique topology reveals intrinsic geometric structure in neural correlations
• Higher-order interactions in complex networks of phase oscillators promote abrupt synchronization switching
• Abrupt Desynchronization and Extensive Multistability in Globally Coupled Oscillator Simplices
• Social contagion models on hypergraphs
• Simplicial SIS model in scale-free uniform hypergraph
• Hopf normal form with $S_N$ symmetry and reduction to systems of nonlinearly coupled phase oscillators
• Fitness for Synchronization of Network Motifs
• D-dimensional oscillators in simplicial structures: odd and even dimensions display different synchronization scenarios
• Complexity reduction in the 3D Kuramoto model
• Phase chimera states on non-local hyperrings
• Generalized frustration in the multidimensional Kuramoto model
• Exploring the phase diagrams of multidimensional Kuramoto models
• Global synchronization on time-varying higher-order structures

Cited by in corpus (3)

• Bifurcations in the Kuramoto model with external forcing and higher-order interactions
• Exact solutions of the Kuramoto model with asymmetric higher order interactions of arbitrary order
• On the efficiency of pairwise Hamiltonian control to desynchronize the higher-order Kuramoto model