Effect of discrete time observations on synchronization in Chua model and applications to data assimilation

TL;DR

This study investigates how observational frequency and noise affect synchronization and prediction accuracy in the Chua circuit model, revealing limitations based on coupling variables, noise levels, and observation intervals.

Contribution

It provides new insights into the effects of discrete-time observations and noise on synchronization in a low-dimensional chaotic system, with implications for data assimilation.

Findings

Synchronization occurs only when coupling x and y variables.

Higher noise levels reduce the range of effective coupling.

Prediction errors increase significantly with noisy observations.

Abstract

Recent studies show indication of the effectiveness of synchronization as a data assimilation tool for small or meso-scale forecast when less number of variables are observed frequently. Our main aim here is to understand the effects of changing observational frequency and observational noise on synchronization and prediction in a low dimensional chaotic system, namely the Chua circuit model. We perform {\it identical twin experiments} in order to study synchronization using discrete-in-time observations generated from independent model run and coupled unidirectionally to the model through $x$, $y$ and $z$ separately. We observe synchrony in a finite range of coupling constant when coupling the x and y variables of the Chua model but not when coupling the z variable. This range of coupling constant decreases with increasing levels of noise in the observations. The Chua system does not show synchrony when the time gap between observations is greater than about one-seventh of the Lyapunov time. Finally, we also note that prediction errors are much larger when noisy observations are used than when using observations without noise.