Impact of higher-order coupling functions on synchronization and multistability

Determine which higher-order coupling functions used in generalized Kuramoto oscillator models on higher-order networks—including, for example, the symmetric triadic sin(θ_j + θ_k − 2θ_i) and the asymmetric triadic sin(2θ_j − θ_k − θ_i)—better support synchronization; characterize the forms of multistability that arise from different higher-order coupling functions; and ascertain whether mixtures of multiple higher-order coupling functions produce new collective dynamical phenomena.

Background

The review discusses generalized Kuramoto dynamics with nonpairwise interactions (higher-order coupling) and highlights that different functional forms—such as symmetric and asymmetric triadic terms—can lead to markedly different collective behaviors, including explosive transitions and extensive multistability. Despite widespread use of a few standard nonpairwise coupling functions, there is no consensus on which forms to adopt for general oscillator dynamics.

The authors note that, even for the specific symmetric and asymmetric triadic coupling functions considered, choices are often made for technical convenience, and the consequences for collective dynamics are not fully understood. This motivates a precise determination of how various higher-order coupling functions influence synchronization, the spectrum of multistable states, and whether combining multiple coupling functions yields qualitatively new collective behaviors.