Pinning Synchronization of Coupled Oscillators with Paired Topologies

This paper investigates the pinning synchronization of a group of coupled oscillators, where both the dissipative and restorative interactions are taken into consideration. The paired coupling topologies are introduced to capture this feature of the dynamics. To realize the synchronization of the coupled oscillators, the pinning control is introduced, and two pinning criteria are proposed to ensure the synchronization. Both these two proposed criteria provide sufficient and necessary conditions for pinning synchronization of the coupled oscillators with paired topologies. Simulation examples are illustrated to verify the proposed theoretical results.