Spatio-temporal Bounded Noises, and transitions induced by them in solutions of real Ginzburg-Landau model

TL;DR

This paper introduces two types of spatio-temporal bounded noises and explores their effects on the real Ginzburg-Landau model, revealing unique phase transition phenomena distinct from unbounded noise influences.

Contribution

The study develops new spatio-temporal bounded noises based on Cai-Lin and Tsallis-Borland models and analyzes their impact on phase transitions in the Ginzburg-Landau system.

Findings

Bounded noises influence the distribution from bimodal to unimodal.

Observed inverse 'order-to-disorder' transition.

Detected re-entrant phase transition phenomena.

Abstract

In this work, we introduce two spatio-temporal colored bounded noises, based on the zero-dimensional Cai-Lin and Tsallis-Borland noises. We then study and characterize the dependence of the defined bounded noises on both a temporal correlation parameter $\tau$ and on a spatial coupling parameter $\lambda$. The boundedness of these noises has some consequences on their equilibrium distributions. Indeed in some cases varying $\lambda$ may induce a transition of the distribution of the noise from bimodality to unimodality. With the aim to study the role played by bounded noises on nonlinear dynamical systems, we investigate the behavior of the real Ginzburg-Landau time-varying model additively perturbed by such noises. The observed phase transitions phenomenology is quite different from the one observed when the perturbations are unbounded. In particular, we observed an inverse "order-to-disorder" transition, and a re-entrant transition, with dependence on the specific type of bounded noise.