Transitions from trees to cycles in adaptive flow networks
Martens, Erik A. LU
and Klemm, Konstantin
(2017)
In Frontiers in Physics
5.
- Abstract
Transport networks are crucial to the functioning of natural and technological systems. Nature features transport networks that are adaptive over a vast range of parameters, thus providing an impressive level of robustness in supply. Theoretical and experimental studies have found that real-world transport networks exhibit both tree-like motifs and cycles. When the network is subject to load fluctuations, the presence of cyclic motifs may help to reduce flow fluctuations and, thus, render supply in the network more robust. While previous studies considered network topology via optimization principles, here, we take a dynamical systems approach and study a simple model of a flow network with dynamically adapting weights (conductances).... (More)
Transport networks are crucial to the functioning of natural and technological systems. Nature features transport networks that are adaptive over a vast range of parameters, thus providing an impressive level of robustness in supply. Theoretical and experimental studies have found that real-world transport networks exhibit both tree-like motifs and cycles. When the network is subject to load fluctuations, the presence of cyclic motifs may help to reduce flow fluctuations and, thus, render supply in the network more robust. While previous studies considered network topology via optimization principles, here, we take a dynamical systems approach and study a simple model of a flow network with dynamically adapting weights (conductances). We assume a spatially non-uniform distribution of rapidly fluctuating loads in the sinks and investigate what network configurations are dynamically stable. The network converges to a spatially non-uniform stable configuration composed of both cyclic and tree-like structures. Cyclic structures emerge locally in a transcritical bifurcation as the amplitude of the load fluctuations is increased. The resulting adaptive dynamics thus partitions the network into two distinct regions with cyclic and tree-like structures. The location of the boundary between these two regions is determined by the amplitude of the fluctuations. These findings may explain why natural transport networks display cyclic structures in the micro-vascular regions near terminal nodes, but tree-like features in the regions with larger veins.
(Less)
- author
- Martens, Erik A.
LU
and Klemm, Konstantin
- publishing date
- 2017-11-28
- type
- Contribution to journal
- publication status
- published
- keywords
- Adaptive networks, Cycles, Flow networks, Heterogeneous network structures, Loops, Transcritical bifurcation, Transport networks, Tree-like structures
- in
- Frontiers in Physics
- volume
- 5
- article number
- 62
- publisher
- Frontiers Media S. A.
- external identifiers
-
- scopus:85043718620
- ISSN
- 2296-424X
- DOI
- 10.3389/fphy.2017.00062
- language
- English
- LU publication?
- no
- additional info
- Funding Information: EM would like to thank J. C. Brings Jacobsen for helpful discussions on circulatory physiology and E. Katifori on adaptive networks. We acknowledge travel funding from Action CA15109, European Cooperation for Statistics of Network Data Science (COSTNET). Research conducted by EM is supported by the Dynamical Systems Interdisciplinary Network, University of Copenhagen. KK acknowledges funding from MINECO through the Ram?n y Cajal program and through project SPASIMM, FIS2016-80067-P (AEI/FEDER, EU). Publisher Copyright: © 2017 Martens and Klemm. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.
- id
- 4170370d-74b1-4fd2-acfb-a65e0fdf5dcc
- date added to LUP
- 2021-03-19 21:23:37
- date last changed
- 2022-04-19 05:22:48
@article{4170370d-74b1-4fd2-acfb-a65e0fdf5dcc,
abstract = {{<p>Transport networks are crucial to the functioning of natural and technological systems. Nature features transport networks that are adaptive over a vast range of parameters, thus providing an impressive level of robustness in supply. Theoretical and experimental studies have found that real-world transport networks exhibit both tree-like motifs and cycles. When the network is subject to load fluctuations, the presence of cyclic motifs may help to reduce flow fluctuations and, thus, render supply in the network more robust. While previous studies considered network topology via optimization principles, here, we take a dynamical systems approach and study a simple model of a flow network with dynamically adapting weights (conductances). We assume a spatially non-uniform distribution of rapidly fluctuating loads in the sinks and investigate what network configurations are dynamically stable. The network converges to a spatially non-uniform stable configuration composed of both cyclic and tree-like structures. Cyclic structures emerge locally in a transcritical bifurcation as the amplitude of the load fluctuations is increased. The resulting adaptive dynamics thus partitions the network into two distinct regions with cyclic and tree-like structures. The location of the boundary between these two regions is determined by the amplitude of the fluctuations. These findings may explain why natural transport networks display cyclic structures in the micro-vascular regions near terminal nodes, but tree-like features in the regions with larger veins.</p>}},
author = {{Martens, Erik A. and Klemm, Konstantin}},
issn = {{2296-424X}},
keywords = {{Adaptive networks; Cycles; Flow networks; Heterogeneous network structures; Loops; Transcritical bifurcation; Transport networks; Tree-like structures}},
language = {{eng}},
month = {{11}},
publisher = {{Frontiers Media S. A.}},
series = {{Frontiers in Physics}},
title = {{Transitions from trees to cycles in adaptive flow networks}},
url = {{http://dx.doi.org/10.3389/fphy.2017.00062}},
doi = {{10.3389/fphy.2017.00062}},
volume = {{5}},
year = {{2017}},
}