Effect of noise on the synchronization of bidirectionally coupled time-delayed systems

Effect of noise on synchronization of bidirectionally coupled Ikeda systems is investigated. Sufficient conditions for the complete synchronization are rigorously established by means of the so-called LaSalle-type invariance principle for stochastic differential equations. Numerical simulations are provided to illustrate the effectiveness of the theoretical results. The simulation results show that the average error in synchronization exhibits a nonmonotonic behavior with the noise amplitude. Furthermore, the simulation results show that synchronization of identical time-delayed systems subjected to the common noise can be achieved for large enough noise amplitudes.