Phase transition to synchronization in generalized Kuramoto model with low-pass filter

A second-order continuous synchronization has been well documented for the classic Kuramoto model. Here we generalize the classic Kuramoto model by incorporating a low-pass filter (LPF) in the coupling, which serves as a simple form of indirect coupling through a common external dynamic environment. We uncover that a first-order explosive synchronization turns out to be a very generic phenomenon in this generalized Kuramoto model with LPF. We establish theoretical results by providing a rigorous analytical treatment, which is validated by conducting extensive numerical simulations. Our study provides a new root for the emergence of first-order explosive synchronization, which could substantially deepen the understanding of the underlying mechanism of a first-order phase transition towards synchronization in coupled dynamical networks.