Synchronization of spatiotemporal chaos and reservoir computing via scalar signals

Abstract

Reservoir computing turns out to be a powerful data-driven tool for model-free prediction and synchronization of chaotic systems. However, recent studies of synchronization using reservoir computing mainly focus on low-dimensional chaotic systems, the relevant research on spatiotemporally chaotic systems that are more common in nature is still missing. Here, we investigate synchronization of spatiotemporally chaotic systems via reservoir computing instead of dynamical equations. By transmitting scalar driving signals at a finite number of spatial points, we realize three types of synchronization, including the one between the trained reservoir computer and its learned spatiotemporally chaotic system, the one between the trained reservoir computers, and the cascading one among the learned system and the trained reservoir computers. Our method can not only be used to confirm whether the trained reservoir computer has captured the features of the spatiotemporally chaotic system but also is of great significance for application in complex networks and secure communication. The results are illustrated numerically with two benchmark dynamical systems.