Impact of second-order coupling functions on desynchronization in the Higher-Order Kuramoto model

Determine how the two second-order coupling functions sin(θj + θk − 2θi) and sin(2θj − θk − θi), considered in the higher-order Kuramoto model with triadic interactions, affect the emergence and robustness of desynchronized dynamics, beyond their known difference in convergence speed near synchronization.

Background

The paper studies a higher-order Kuramoto model (HOKM) that includes both pairwise and triadic interaction terms. For triadic interactions, the literature commonly uses either sin(θj + θk − 2θi) or sin(2θj − θk − θi) as the second-order coupling function, and phase-reduction analyses sometimes produce weighted combinations of both.

Near the synchronization manifold, these two coupling functions are known to differ only in the speed of convergence toward synchronization, with one being twice as fast. However, the authors explicitly note that their impact on desynchronization dynamics remains an open question, which is important for understanding and designing methods that aim to reduce synchronization.