Spatio-temporal sine-Wiener bounded noise and its effect on Ginzburg-Landau model

In this work we introduce a spatio-temporal bounded noise derived by the sine-Wiener noise and by the spatially colored unbounded noise proposed by Garcia-Ojalvo, Sancho, and Ramirez-Piscina (GSR noise). We characterize the behavior of the equilibrium distribution of this novel noise by showing its dependence on both the temporal and the spatial autocorrelation lengths. In particular, we show that the distribution experiences a stochastic transition from bimodality to trimodality. Then, we employ the noise here defined to study the emergence of phase transitions in the real Ginzburg-Landau model. Various phenomena are evidenced by means of numerical simulations, among which reentrant transitions, as well as differences in the response of the system to equivalent GSR additive noise perturbations.