Synchronization of networked harmonic oscillators under nonlinear protocols

This paper deals with the synchronization of networked harmonic oscillators under nonlinear protocols. Some convergence analysis for such networked harmonic oscillators, both without and with a leader, are provided by means of algebraic graph theory, matrix theory and Lyapunov stability theory on dynamical systems. We show that the networked harmonic oscillators can achieve synchronization under nonlinear control input. Moreover, we also demonstrate that all harmonic oscillators can attain the position and velocity of the leader under nonlinear network connectivity conditions. Finally, numerical simulations are given to verify the correctness of obtained results.