Approximation methods for the stability of complete synchronization on duplex networks

TL;DR

This paper introduces two approximation methods to analyze the stability of complete synchronization in duplex networks, enhancing prediction accuracy especially for large networks.

Contribution

It proposes two novel approximation techniques, including a modified master stability function and a focus on key unstable modes, for assessing synchronization stability.

Findings

Both methods accurately predict stability in small networks.

The second method remains effective for large networks.

The second method simplifies analysis by focusing on dominant unstable modes.

Abstract

Recently, the synchronization on multi-layer networks has drawn a lot of attention. In this work, we study the stability of the complete synchronization on duplex networks. We investigate effects of coupling function on the complete synchronization on duplex networks. We propose two approximation methods to deal with the stability of the complete synchronization on duplex networks. In the first method, we introduce a modified master stability function and, in the second method, we only take into consideration the contributions of a few most unstable transverse modes to the stability of the complete synchronization. We find that both methods work well for predicting the stability of the complete synchronization for small networks. For large networks, the second method still works pretty well.