Global generalized synchronization in networks of different time-delay systems

TL;DR

This paper demonstrates the existence of global generalized synchronization in diverse time-delay systems with different structures and dimensions, revealing a common synchronization manifold and providing stability conditions, which could aid in controlling pathological synchrony.

Contribution

It introduces the concept of global generalized synchronization across different time-delay systems and derives an analytical stability condition using Krasvoskii-Lyapunov theory.

Findings

Global GS exists in different time-delay systems with varying dimensions.

A smooth transformation maps systems to a common GS manifold.

An analytical stability condition for GS is established.

Abstract

We show that global generalized synchronization (GS) exists in structurally different time-delay systems, even with different orders, with quite different fractal (Kaplan-Yorke) dimensions, which emerges via partial GS in symmetrically coupled regular networks. We find that there exists a smooth transformation in such systems, which maps them to a common GS manifold as corroborated by their maximal transverse Lyapunov exponent. In addition, an analytical stability condition using the Krasvoskii-Lyapunov theory is deduced. This phenomenon of GS in strongly distinct systems opens a new way for an effective control of pathological synchronous activity by means of extremely small perturbations to appropriate variables in the synchronization manifold.