SYNCHRONIZATION IN NETWORKS OF COUPLED HARMONIC OSCILLATORS WITH STOCHASTIC PERTURBATION AND TIME DELAYS

In this paper, we investigate the leader-follower synchronization ofcoupled second-order linear harmonic oscillators with the presence ofrandom noises and time delays. The interaction topology is modeledby a weighted directed graph and the weights are perturbed by whitenoise. On the basis of stability theory of stochastic differential delayequations, algebraic graph theory and matrix theory, we show that thecoupled harmonic oscillators can be synchronized almost surely withrandom perturbation and time delays. Numerical examples are presentedto illustrate our theoretical results.