Impact of Channel Dynamics on Higher-order Interactions of Oscillators

Modeling higher-order interactions (HOIs) in nonlinear networks with static topologies is often physically restrictive. We demonstrate that standard 3-body Kuramoto couplings are mathematically equivalent to pairwise connections modulated by latent variables of transmission channels. While standard HOI topologies emerge in the adiabatic limit of these variables, relaxing this constraint reveals that latent channel timescales dictate collective macroscopic states. Specifically, transmission inertia drives bistability for symmetric interaction tensors and anti-phase cluster synchronization for antisymmetric ones. Furthermore, dynamically induced clustering in global topologies emerges as a finite-size effect of the dynamics of the local channels. Ultimately, we show that relying exclusively on static topologies restricts interaction modeling. Integrating latent variables captures the transient inertia and fundamental asymmetry of physical networks, bridging the analytical utility of higher-order functions with the reality of the underlying transmission medium.