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Emergence of higher-order interactions in systems of coupled Kuramoto oscillators with time delay
Narumi Fujii1,2, Keisuke Taga1,3, Riccardo Muolo1,4
1Institute of Science Tokyo, Department of Systems and Control Engineering, (Former Tokyo Tech), Tokyo 152-8552, Japan.
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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