A taxonomy for generalized synchronization between flat-coupled systems

TL;DR

This paper introduces a taxonomy for generalized synchronization in flat-coupled systems, analyzing how coupling strength and system properties influence synchronization types and their topological conjugacy.

Contribution

It proposes a new taxonomy for generalized synchronization based on coupling strength, system dimensions, and dissipation, with a focus on flat control law coupling.

Findings

First-return maps can be topologically conjugate in some cases

Response map can be foliated while drive map is not

Synchronization types depend on coupling strength and system properties

Abstract

Generalized synchronization is plausibly the most complex form of synchronization. Previous studies have revealed the existence of weak or strong forms of generalized synchronization depending on the multi- or mono-valued nature of the mapping between the attractors of two unidirectionally-coupled systems. Generalized synchronization is here obtained by coupling two systems with a flat control law. Here, we demonstrate that the corresponding first-return maps can be topologically conjugate in some cases. Conversely, the response map can foliated while the drive map is not. We describe the corresponding types of generalized synchronization, explicitly focusing on the influence of the coupling strength when significantly different dimensions or dissipation properties characterize the coupled systems. A taxonomy of generalized synchronization based on these properties is proposed.