Designing temporal networks that synchronize under resource constraints

Yuanzhao Zhang,Steven H Strogatz

doi:10.1038/s41467-021-23446-9

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.

Highlights

Being fundamentally a non-equilibrium process, synchronization comes with unavoidable energy costs and has to be maintained under the constraint of limited resources
Can temporal variations synchronize systems beyond the fundamental limit set by the optimal static networks? This question is especially interesting given that past studies have often focused on the fast-switching limit, for which the network structure changes much faster than the node dynamics
The results above provide new insights into the intriguing phenomenon that certain temporal networks only synchronize for intermediate switching rate[21,26,27]: when switching is too fast, the temporal network reduces to its static counterpart and one cannot take full advantage of the temporal variation in the connections; when switching is too slow, the asymptotic stability might be maximized, the system would have desynchronized long before the network experiences any meaningful change

Summary

Introduction

Being fundamentally a non-equilibrium process, synchronization comes with unavoidable energy costs and has to be maintained under the constraint of limited resources. Can temporal variations synchronize systems beyond the fundamental limit set by the optimal static networks? These fast-switching networks are equivalent to their static, time-averaged counterparts in terms of synchronization stability[17,23,24,25].

Results

Conclusion