Better Synchronizability Predicted by Crossed Double Cycle

TL;DR

This paper introduces crossed double cycle networks, demonstrating that their synchronizability can be significantly improved by adjusting a parameter, with eigenratio R closely related to average distance L, following a power-law.

Contribution

The study proposes a new network model called crossed double cycles and analyzes how their synchronizability depends on network parameters and average distance.

Findings

Eigenratio R is highly sensitive to average distance L.

Adjusting crossed length m enhances synchronizability.

Eigenratio R follows a power-law relation R ~ L^{1.5}.

Abstract

In this brief report, we propose a network model named crossed double cycles, which are completely symmetrical and can be considered as the extensions of nearest-neighboring lattices. The synchronizability, measured by eigenratio $R$, can be sharply enhanced by adjusting the only parameter, crossed length $m$. The eigenratio $R$ is shown very sensitive to the average distance $L$, and the smaller average distance will lead to better synchronizability. Furthermore, we find that, in a wide interval, the eigenratio $R$ approximately obeys a power-law form as $R\sim L^{1.5}$.