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  Quantifying transient spreading dynamics on networks

Wolter, J., Lünsmann, B., Zhang, X., Schröder, M., & Timme, M. (2018). Quantifying transient spreading dynamics on networks. Chaos, 28(6): 063122. doi:10.1063/1.5000996.

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Genre: Journal Article

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 Creators:
Wolter, J., Author
Lünsmann, B., Author
Zhang, Xiaozhu1, Author              
Schröder, M., Author
Timme, Marc1, Author              
Affiliations:
1Max Planck Research Group Network Dynamics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society, ou_2063295              

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 Abstract: Spreading phenomena on networks are essential for the collective dynamics of various natural and technological systems, from information spreading in gene regulatory networks to neural circuits or from epidemics to supply networks experiencing perturbations. Still, how local disturbances spread across networks is not yet quantitatively understood. Here we analyze generic spreading dynamics in deterministic network dynamical systems close to a given operating point. Standard dynamical systems' theory does not explicitly provide measures for arrival times and amplitudes of a transient, spreading signal because it focuses on invariant sets, invariant measures and other quantities less relevant for transient behavior. We here change the perspective and introduce effective expectation values for deterministic dynamics to work out a theory explicitly quantifying when and how strongly a perturbation initiated at one unit of a network impacts any other. The theory provides explicit timing and amplitude information as a function of the relative position of initially perturbed and responding unit as well as on the entire network topology.

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Language(s): eng - English
 Dates: 2018-06-212018-06
 Publication Status: Published in print
 Pages: -
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 Table of Contents: -
 Rev. Type: Peer
 Identifiers: DOI: 10.1063/1.5000996
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Title: Chaos
Source Genre: Journal
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Pages: 14 Volume / Issue: 28 (6) Sequence Number: 063122 Start / End Page: - Identifier: -