Rotation number, stochastic resonance, and synchronization of coupled systems without periodic driving

This article investigates the influence of noise in a two-dimensional square array of coupled nonlinear oscillators without periodic driving. Array enhanced stochastic resonance under global as well as local noise perturbation is shown to exist under a crucial condition: the value of the rotation number of the deterministic system being zero. Meanwhile, the stochastic synchronization phenomenon is displayed in a wide range of noise intensity whether noise is added globally or locally. Furthermore, for every oscillator, the peak frequency is shown to agree with the rotation number much better than in the uncoupled system.