Asymptotic behavior of the Kuramoto system with periodic natural frequency (Q2054013)

The Kuramoto model is a fundamental and well-known model for studying synchronization of oscillators. This work studies an all-to-all coupled Kuramoto-type model \[\theta_i'=\omega_i(t)+\frac{K}{N}\sum_{k=1}^N \sin(\theta_k-\theta_i), \;\;\;1\leq i\leq N\] in which the natural frequencies \(\omega_i(t)\) of each of the oscillators varies periodically in time, with common period \(T\). Assuming that the coupling constant \(K\) is sufficeintly large, the authors prove the existence of a solution for which the differences \(\theta_i-\theta_j\) are \(T\)-periodic. The asymptotic behavior of the system is then characterized as the sum of a time-periodic solution, a drift term, and an exponentially decaying term. The theoretical results proved are illustrated by numerical simulations.