Synchronization of the generalized Kuramoto model with time delay and frustration

We studied the collective behaviors of the time-delayed Kuramoto model with frustration under general network topology. For the generalized Kuramoto model with the graph diameter no greater than two and under a sufficient regime in terms of small time delay and frustration and large coupling strength, we showed that the complete frequency synchronization occurs exponentially fast when the initial configuration is distributed in a half circle. We also studied a complete network, which is a small perturbation of all-to-all coupling, as well as presented sufficient frameworks leading to the exponential emergence of frequency synchronization for the initial data confined in a half circle.