Synchronizing spatio-temporal chaos with imperfect models: a stochastic surface growth picture

TL;DR

This paper models the synchronization error in imperfect spatially extended systems as a rough surface described by the KPZ equation with bounds, revealing universal behavior across different imperfections.

Contribution

It introduces a novel surface growth framework using the KPZ equation to analyze synchronization errors caused by model imperfections in spatial systems.

Findings

Synchronization error resembles a KPZ surface with bounds.

Both parameter mismatch and unresolved scales lead to similar error behavior.

Results are consistent across various systems and imperfections.

Abstract

We study the synchronization of two spatially extended dynamical systems where the models have imperfections. We show that the synchronization error across space can be visualized as a rough surface governed by the Kardar-Parisi-Zhang equation with both upper and lower bounding walls corresponding to nonlinearities and model discrepancies, respectively. Two types of model imperfections are considered: parameter mismatch and unresolved fast scales, finding in both cases the same qualitative results. The consistency between different setups and systems indicates the results are generic for a wide family of spatially extended systems.