Optimizing synchronization in multiplex networks of phase oscillators

TL;DR

This paper introduces an analytical method to optimize synchronization in multiplex networks of phase oscillators by deriving a synchrony alignment function that incorporates structural and dynamical properties, enabling perfect synchronization.

Contribution

The paper develops the multiplex synchrony alignment function (MSAF) to analytically determine optimal frequencies for synchronization in multiplex networks, including frustrated and non-frustrated oscillators.

Findings

Perfect synchronization can be achieved in a network layer under certain conditions.

The MSAF effectively predicts optimal frequencies for synchronization.

The scheme is validated on heterogeneous Kuramoto multiplex networks.

Abstract

We present an analytical scheme to achieve optimal synchronization in multiplex networks of frustrated and non-frustrated phase oscillators. We derive a multiplex synchrony alignment function (MSAF) for that purpose, the expression of which consists of structural as well as dynamical information of the layers of the multiplex network. Analyzing the MSAF, a set of frequencies (optimal frequencies) is determined to achieve optimal synchronization in the network. Further, using the scheme, we show that perfect synchronization can be achieved in a layer of the multiplex network for given coupling strength and phase frustration parameters. The analytical scheme presented here has been tested for heterogeneous multiplex networks of frustrated and non-frustrated Kuramoto dynamics.