Spatiotemporal sine-Wiener Bounded Noise and its effect on Ginzburg-Landau model

TL;DR

This paper introduces a new spatiotemporal bounded noise based on sine-Wiener and GSR noises, analyzing its distribution and effects on phase transitions in the Ginzburg-Landau model, revealing complex phenomena like re-entrant transitions.

Contribution

The study develops a novel spatiotemporal bounded noise model and investigates its impact on phase transitions in the Ginzburg-Landau system, highlighting unique stochastic behaviors.

Findings

Distribution transitions from bimodality to trimodality

Re-entrant phase transitions observed

Differences in system response to various noise types

Abstract

In this work, we introduce a kind of spatiotemporal bounded noise derived by the sine-Wiener noise and by the spatially colored unbounded noise introduced by Garc\'ia-Ojalvo, Sancho and Ram\'irez-Piscina (GSR noise). We characterize the behavior of the distribution of this novel noise by showing its dependence on both the temporal and the spatial autocorrelation strengths. In particular, we show that the distribution experiences a stochastic transition from bimodality to trimodality. Then, we employ the noise here defined to study phase transitions on Ginzburg-Landau model. Various phenomena are evidenced by means of numerical simulations, among which re-entrant transitions, as well as differences in the response of the system to GSR noise additive perturbations. Finally, we compare the statistical behaviors induced by the sine-Wiener noise with those caused by 'equivalent' GSR noises.