Designing temporal networks that synchronize under resource constraints

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.

published version

References in corpus (9)

• The Magnus expansion and some of its applications
• Adaptive Coevolutionary Networks: A Review
• Path lengths, correlations, and centrality in temporal networks
• Maximum Performance at Minimum Cost in Network Synchronization
• Nonequilibrium thermodynamics of coupled molecular oscillators: The energy cost and optimal design for synchronization
• The theory of Turing patterns on time varying networks
• Birth and stabilization of phase clusters by multiplexing of adaptive networks
• Experiments with arbitrary networks in time-multiplexed delay systems
• Stabilizing Stuart-Landau oscillators via time-varying networks

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• Compressing the chronology of a temporal network with graph commutators