Generalized synchronization in relay systems with instantaneous coupling

TL;DR

This paper investigates generalized synchronization in relay systems with instantaneous coupling, analyzing Lyapunov spectra, quantifying synchronization with nonlinear measures, and demonstrating robustness through experiments.

Contribution

It provides a comprehensive analysis of generalized synchronization in relay systems, combining theoretical, numerical, and experimental approaches.

Findings

Complete synchronization occurs at a critical coupling strength.

Generalized synchronization with the relay system also appears at this point.

The proposed nonlinear measures effectively quantify generalized synchronization.

Abstract

We demonstrate the existence of generalized synchronization in systems that act as mediators between two dynamical units that, in turn, show complete synchronization with each other. These are the so-called relay systems. Specifically, we analyze the Lyapunov spectrum of the full system to elucidate when complete and generalized synchronization appear. We show that once a critical coupling strength is achieved, complete synchronization emerges between the systems to be synchronized, and at the same point, generalized synchronization with the relay system also arises. Next, we use two nonlinear measures based on the distance between phase-space neighbors to quantify the generalized synchronization in discretized time series. Finally, we experimentally show the robustness of the phenomenon and of the theoretical tools here proposed to characterize it.