Large-Time Dynamics of Kuramoto Oscillators under the Effects of Inertia and Frustration

We study the intricate interplay between inertial effect and interaction frustration in an ensemble of Kuramoto oscillators. In particular, we discuss how asymptotic synchronization can arise from the competition between synchronization factors such as strong coupling strength and desynchronization factors such as inertia and frustration. We provide several frameworks in terms of system parameters and initial configurations that guarantee the emergence of complete synchronization. For a restricted class of initial configurations, we show that asymptotic complete synchronization occurs exponentially fast and its exponential decay rate depends on the strength of system parameters such as coupling, inertia, and frustration. We also provide several numerical simulations and compare these with analytical results.