Designing temporal networks that synchronize under resource constraints

TL;DR

This paper demonstrates that temporal variation in network structure can enhance synchronization efficiency under resource constraints, outperforming static networks, and provides analytical insights into the underlying mechanisms.

Contribution

It introduces a novel open-loop design for temporal networks that improves synchronization under limited resources and links this effect to the curvature of the master stability function.

Findings

Temporal networks can synchronize systems with limited resources.

Switching rate influences synchronization effectiveness.

Analytical link between topology dynamics and stability established.

Abstract

Being fundamentally a non-equilibrium process, synchronization comes with unavoidable energy costs and has to be maintained under the constraint of limited resources. Such resource constraints are often reflected as a finite coupling budget available in a network to facilitate interaction and communication. Here, we show that introducing temporal variation in the network structure can lead to efficient synchronization even when stable synchrony is impossible in any static network under the given budget, thereby demonstrating a fundamental advantage of temporal networks. The temporal networks generated by our open-loop design are versatile in the sense of promoting synchronization for systems with vastly different dynamics, including periodic and chaotic dynamics in both discrete-time and continuous-time models. Furthermore, we link the dynamic stabilization effect of the changing topology to the curvature of the master stability function, which provides analytical insights into synchronization on temporal networks in general. In particular, our results shed light on the effect of network switching rate and explain why certain temporal networks synchronize only for intermediate switching rate.