A semi-analytic method for computing the long-time order parameter dynamics in mean-field coupled overdamped oscillators with colored noises

The order parameter dynamics of a mean-field model is frequently investigated in macroscopic cumulant dynamics, from which a bifurcation can be predicted qualitatively. In this Letter, for quantitatively investigating the long-time order parameter dynamics, a semi-analytic method is proposed based on approximate nonlinear Fokker-Planck equations. Applying the new method to the mean-field model of periodically driven overdamped bistable oscillators with colored noise, we exhibit the bifurcation behavior and the nonlinear stochastic resonance of the order parameter by tuning noise intensity or coupling coefficient, and the accuracy of the new method are verified by direct simulation. Our observations disclose some new properties about the order parameter dynamics of the mean-field model. For example, the periodic signal shifts the critical coupling coefficient to a larger value, while the nonzero correlation time of the colored noise shifts it to a lower value. Our observation also discloses that there is no quantitatively corresponding relation between the resonant peak and the critical bifurcation parameter of the Gaussian moment system.