Emergence of a common generalized synchronization manifold in network motifs of structurally different time-delay systems

TL;DR

This paper investigates the transition from partial to global generalized synchronization in structurally different time-delay systems, revealing a common synchronization manifold and its relation to phase synchronization.

Contribution

It extends previous findings of a common GS manifold to systems with different orders, using Lyapunov exponents and recurrence analysis for validation.

Findings

Existence of a transition from partial to global GS in diverse time-delay systems.

Confirmation of a common GS manifold across systems of different orders.

Correlation between GS and PS established through multiple analytical methods.

Abstract

We point out the existence of a transition from partial to global generalized synchronization (GS) in symmetrically coupled structurally different time-delay systems of different orders using the auxiliary system approach and the mutual false nearest neighbor method. The present authors have recently reported that there exists a common GS manifold even in an ensemble of structurally nonidentical scalar time-delay systems with different fractal dimensions and shown that GS occurs simultaneously with phase synchronization (PS). In this paper we confirm that the above result is not confined just to scalar one-dimensional time-delay systems alone but there exists a similar type of transition even in the case of time-delay systems with different orders. We calculate the maximal transverse Lyapunov exponent to evaluate the asymptotic stability of the complete synchronization manifold of each of the main and the corresponding auxiliary systems, which in turn ensures the stability of the GS manifold between the main systems. Further we estimate the correlation coefficient and the correlation of probability of recurrence to establish the relation between GS and PS. We also calculate the mutual false nearest neighbor parameter which doubly confirms the occurrence of the global GS manifold.