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In this paper, we investigate synchronization of coupled second-order linearharmonic oscillators with random noises and time delays. The interactiontopology is modeled by a weighted directed graph and the weights are perturbedby white noise. On the basis of stability theory of stochastic differentialdelay equations, algebraic graph theory and matrix theory, we show that thecoupled harmonic oscillators can be synchronized almost surely withperturbation and time delays. Numerical examples are presented to illustrateour theoretical results.

Synchronization in Networks of Coupled Harmonic Oscillators with Stochastic Perturbation and Time Delays