Phase Synchronization on Spacially Embeded Duplex Networks with Total Cost Constraint

TL;DR

This paper studies how spatial structure and inter-layer interactions influence synchronization in duplex networks of Kuramoto oscillators with total cost constraints, revealing that inter-layer coupling enhances synchronization.

Contribution

It introduces analysis of synchronization in duplex Li networks with spatially embedded structures and total cost constraints, highlighting the role of inter-layer interactions.

Findings

Inter-layer interaction significantly enhances synchronizability.

Regular lattice structures are less synchronizable than small-world or random networks.

Sparse inter-links can induce global synchronization similarly to dense inter-links.

Abstract

Synchronization on multiplex networks have attracted increasing attention in the past few years. We investigate collective behaviors of Kuramoto oscillators on single layer and duplex spacial networks with total cost restriction, which was introduced by Li et. al [Li G., Reis S. D., Moreira A. A., Havlin S., Stanley H. E. and Jr A. J., {\it Phys. Rev. Lett.} 104, 018701 (2010)] and termed as the Li network afterwards. In the Li network model, with the increase of its spacial exponent, the network's structure will vary from the random type to the small-world one, and finally to the regular lattice.We first explore how the spacial exponent influences the synchronizability of Kuramoto oscillators on single layer Li networks and find that the closer the Li network is to a regular lattice, the more difficult for it to evolve into synchronization. Then we investigate synchronizability of duplex Li networks and find that the existence of inter-layer interaction can greatly enhance inter-layer and global synchronizability. When the inter-layer coupling strength is larger than a certain critical value, whatever the intra-layer coupling strength is, the inter-layer synchronization will always occur. Furthermore, on single layer Li networks, nodes with larger degrees more easily reach global synchronization, while on duplex Li networks, this phenomenon becomes much less obvious. Finally, we study the impact of inter-link density on global synchronization and obtain that sparse inter-links can lead to the emergence of global synchronization for duplex Li networks just as dense inter-links do. In a word, inter-layer interaction plays a vital role in determining synchronizability for duplex spacial networks with total cost constraint.