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Synchronization dynamics in non-normal networks: the trade-off for optimality

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posted on 2022-08-22, 10:55 authored by Riccardo Muolo, Timoteo Carletti, James GleesonJames Gleeson, Malbor Asllani
Synchronization is an important behavior that characterizes many natural and human made systems that are composed by several interacting units. It can be found in a broad spectrum of applications, ranging from neuroscience to power-grids, to mention a few. Such systems synchronize because of the complex set of coupling they exhibit, with the latter being modeled by complex networks. The dynamical behavior of the system and the topology of the underlying network are strongly intertwined, raising the question of the optimal architecture that makes synchronization robust. The Master Stability Function (MSF) has been proposed and extensively studied as a generic framework for tackling synchronization problems. Using this method, it has been shown that, for a class of models, synchronization in strongly directed networks is robust to external perturbations. Recent findings indicate that many real-world networks are strongly directed, being potential candidates for optimal synchronization. Moreover, many empirical networks are also strongly non-normal. Inspired by this latter fact in this work, we address the role of the non-normality in the synchronization dynamics by pointing out that standard techniques, such as the MSF, may fail to predict the stability of synchronized states. We demonstrate that, due to a transient growth that is induced by the structure’s non normality, the system might lose synchronization, contrary to the spectral prediction. These results lead to a trade-off between non-normality and directedness that should be properly considered when designing an optimal network, enhancing the robustness of synchronization.

Funding

Dynamics of the metabolic state in the context of a systematic approach to the study of the processes of growth and development of higher plants and fungi

Russian Foundation for Basic Research

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Development of theoretical and experimental criteria for predicting the wear resistance of austenitic steels and nanostructured coatings based on a hard alloy under conditions of erosion-corrosion wear

Russian Foundation for Basic Research

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History

Publication

Entropy;23,(36)

Publisher

MDPI

Note

peer-reviewed

Other Funding information

SFI

Language

English

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