Nearest Neighbors, Phase Tubes And Generalized Synchronization

TL;DR

This paper refines the understanding of generalized chaotic synchronization, introducing the phase tube approach to better detect and analyze this regime in physical systems, with potential for new applications.

Contribution

It reveals that state vectors in generalized synchronization are related by a functional relation, not the previously assumed relation, and proposes the phase tube method for studying this phenomenon.

Findings

Refined the concept of generalized synchronization.

Introduced the phase tube approach for detection.

Potential for new applications in physical systems.

Abstract

In this paper we report for the first time on the necessity of the refinement of the concept of generalized chaotic synchronization. We show that the state vectors of the interacting chaotic systems being in the generalized synchronization regime are related with each other by the functional, but not the functional relation as it was assumed until now. We propose the phase tube approach explaining the essence of generalized synchronization and allowing the detection and the study of this regime in many relevant physical circumstances. The finding discussed in this Report gives a strong potential for new applications.