Standard 3-body Kuramoto couplings are mathematically equivalent to pairwise connections through latent transmission channels, and relaxing the adiabatic limit reveals symmetry-dependent bistability and finite-size clustering effects.
Emergence of higher-order interactions in systems of coupled Kuramoto oscillators with time delay
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abstract
We show that higher-order interactions naturally emerge from time-delayed pairwise coupling in Kuramoto oscillators. By expanding the delayed pairwise coupling to the second order, we derive a delay-free Kuramoto model possessing both pairwise and three-body interactions. Numerical simulations and stability analysis demonstrate that the three-body Kuramoto model and the time-delayed pairwise Kuramoto model exhibit qualitatively consistent synchronization transitions under appropriate conditions. In particular, the bistability arising in the time-delayed Kuramoto model is accounted for by the three-body interactions. Our findings reveal that time delays can be recast effectively as higher-order interactions, providing an insight into how coupling delays shape collective dynamics.
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Impact of Channel Dynamics on Higher-order Interactions of Oscillators
Standard 3-body Kuramoto couplings are mathematically equivalent to pairwise connections through latent transmission channels, and relaxing the adiabatic limit reveals symmetry-dependent bistability and finite-size clustering effects.