Analysis of transient stability of coupled Kuramoto oscillators with asymmetric time delays and phase shifts

In this paper, a second-order coupled Kuramoto oscillators with phase shifts and asymmetric delays are investigated under an connected directed network topology. By using a singular perturbation analysis, an equivalent form of a second-order Kuramoto oscillator system is obtained. Some sufficient conditions for the frequency and phase synchronization of such kind of Kuramoto oscillator systems are obtained analytically. Finally, the validity and correctness of the results are further verified by some numerical simulations.