Quasi-Synchronization in Heterogeneous Harmonic Oscillators with Continuous and Sampled Coupling

This paper studies quasi-synchronization in networked heterogeneous harmonic oscillators. By introducing a leader, two distributed synchronization protocols are first proposed for heterogeneous networks by utilizing continuous real-time information and aperiodic sampled-data information. Then, the sufficient conditions on quasi-synchronization are established for heterogeneous networks coupled with nonidentical harmonic oscillators. It is found that each follower oscillator can converge to a bounded region of the leader by adopting either a continuous-time protocol or sampled-data protocol. The upper bound of the region is solved for networked heterogeneous harmonic oscillators. Finally, an electrical network is provided to illustrate the applicability of the theoretical results, and two examples are provided to illustrate the effectiveness of the sufficient criteria