Frequency Synchronization of Heterogeneous Second-Order Forced Kuramoto Oscillator Networks: A Differential Inequality Approach

This article is concerned with the frequency synchronization of heterogeneous second-order forced Kuramoto oscillator networks. Under this model, each second-order oscillator is driven by a periodic external force, and its dynamics will be affected by the inertia and the damping coefficient. By introducing the second-order differential inequality, we first show that this model exhibits frequency synchronization for any initial data if the amplitude of force is large and the inertia is small. In case that the amplitude of force is not large, we prove that this model still can drive frequency synchronization provided that the coupling strength is large and the initial configuration is confined to a sector. Comparison studies with existing synchronization conditions are made to indicate that these proposed criteria seem to be less conservative. A desynchronization for large inertia is shown in our numerical experiment.