Noise-Induced Periodic Behaviour in the Globally Coupled Complex Ginzburg-Landau Equation

We study the effect of noise in a recently introduced discrete version of the complex Ginzburg-Landau equation which is a globally coupled oscillator model. The response of the previously discovered coherent chaotic state to white noise is investigated. For small noise levels, the mean-field amplitude remains non-zero in the thermodynamic limit, but we find a pronounced increase in the periodicity of its dynamics. For larger noise, a phase transition to a zero mean field is observed. An interpretation of these phenomena is proposed using an equation of motion for a single oscillator with self-consistent forcing.