Enhancement of phase synchronization by an infinite variance noise in a small-world network

In this work, we study the synchronization of a group of identical phase oscillators (rotors) in the small-world (SW) networks, driven by an external random force. The dynamics of the rotors are governed by the Kuramoto model, and the distribution of the noise is given by a Cauchy–Lorentz probability density function with zero mean and the width $$\gamma $$ . We find that the partially phase-synchronized states of identical oscillators (with $$\gamma =0)$$ in the SW network become more synchronized when $$\gamma $$ increases to an optimum value, where the phase synchrony in the system reaches a maximum and then start to fall. We discuss that the reason for this “stochastic synchronization” is the weakening and destruction of topological defects presented in the partially phase-synchronized attractors of the Kuramoto model in SW network of identical oscillators.