Stochastic feedback coupling synchronization of networked harmonic oscillators

This paper presents a stochastic feedback coupling strategy for almost sure exponential synchronization of networked harmonic oscillators. Differing from most of existing publications, in which noise is not beneficial to synchronization in complex dynamical networks, a stochastic coupling strategy is designed here by using discrete-time noisy sampled-data to achieve the almost sure exponential synchronization of networked harmonic oscillators. Both leaderless synchronization and leader-following synchronization of networked harmonic oscillators are considered. Some sufficient conditions are established to reach two types of synchronization by employing algebraic graph theory, Itô stochastic integral, stochastic control technique and mathematical analysis. Two numerical simulations are provided to illustrate the effectiveness of the theoretical results.