Cyclic Structure Induced by Load Fluctuations in Adaptive Transportation Networks
Martens, Erik Andreas LU
and Klemm, Konstantin
(2019)
20th European Conference on Mathematics for Industry, ECMI 2018
In Mathematics in Industry
30.
p.147-155
- Abstract
- Transport networks are crucial to the functioning of natural systems and technological infrastructures. For flow networks in many scenarios, such as rivers or blood vessels, acyclic networks (i.e., trees) are optimal structures when assuming time-independent in- and outflow. Dropping this assumption, fluctuations of net flow at source and/or sink nodes may render the pure tree solutions unstable even under a simple local adaptation rule for conductances. Here, we consider tree-like networks under the influence of spatially heterogeneous distribution of fluctuations, where the root of the tree is supplied by a constant source and the leaves at the bottom are equipped with sinks with fluctuating loads. We find that the network divides into... (More)
- Transport networks are crucial to the functioning of natural systems and technological infrastructures. For flow networks in many scenarios, such as rivers or blood vessels, acyclic networks (i.e., trees) are optimal structures when assuming time-independent in- and outflow. Dropping this assumption, fluctuations of net flow at source and/or sink nodes may render the pure tree solutions unstable even under a simple local adaptation rule for conductances. Here, we consider tree-like networks under the influence of spatially heterogeneous distribution of fluctuations, where the root of the tree is supplied by a constant source and the leaves at the bottom are equipped with sinks with fluctuating loads. We find that the network divides into two regions characterized by tree-like motifs and stable cycles. The cycles emerge through transcritical bifurcations at a critical amplitude of fluctuation. For a simple network structure, depending on parameters defining the local adaptation, cycles first appear close to the leaves (or root) and then appear closer towards the root (or the leaves). The interaction between topology and dynamics gives rise to complex feedback mechanisms with many open questions in the theory of network dynamics. A general understanding of the dynamics in adaptive transport networks is essential in the study of mammalian vasculature, and adaptive transport networks may find technological applications in self-organizing piping systems. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/7b0a4840-378e-4c38-8f6c-29b2ac596e94
- author
- Martens, Erik Andreas
LU
and Klemm, Konstantin
- publishing date
- 2019
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- Progress in Industrial Mathematics at ECMI 2018
- series title
- Mathematics in Industry
- editor
- Ferenc, István ; Izsák, Ferenc and Simon, Péter L.
- volume
- 30
- pages
- 147 - 155
- publisher
- Springer
- conference name
- 20th European Conference on Mathematics for Industry, ECMI 2018
- conference location
- Budapest, Hungary
- conference dates
- 2018-06-18 - 2018-06-22
- ISSN
- 2198-3283
- 1612-3956
- ISBN
- 978-3-030-27550-1
- 978-3-030-27549-5
- DOI
- 0.1007/978-3-030-27550-1_19
- language
- English
- LU publication?
- no
- id
- 7b0a4840-378e-4c38-8f6c-29b2ac596e94
- date added to LUP
- 2024-02-28 12:16:35
- date last changed
- 2024-04-03 09:01:02
@inbook{7b0a4840-378e-4c38-8f6c-29b2ac596e94,
abstract = {{Transport networks are crucial to the functioning of natural systems and technological infrastructures. For flow networks in many scenarios, such as rivers or blood vessels, acyclic networks (i.e., trees) are optimal structures when assuming time-independent in- and outflow. Dropping this assumption, fluctuations of net flow at source and/or sink nodes may render the pure tree solutions unstable even under a simple local adaptation rule for conductances. Here, we consider tree-like networks under the influence of spatially heterogeneous distribution of fluctuations, where the root of the tree is supplied by a constant source and the leaves at the bottom are equipped with sinks with fluctuating loads. We find that the network divides into two regions characterized by tree-like motifs and stable cycles. The cycles emerge through transcritical bifurcations at a critical amplitude of fluctuation. For a simple network structure, depending on parameters defining the local adaptation, cycles first appear close to the leaves (or root) and then appear closer towards the root (or the leaves). The interaction between topology and dynamics gives rise to complex feedback mechanisms with many open questions in the theory of network dynamics. A general understanding of the dynamics in adaptive transport networks is essential in the study of mammalian vasculature, and adaptive transport networks may find technological applications in self-organizing piping systems.}},
author = {{Martens, Erik Andreas and Klemm, Konstantin}},
booktitle = {{Progress in Industrial Mathematics at ECMI 2018}},
editor = {{Ferenc, István and Izsák, Ferenc and Simon, Péter L.}},
isbn = {{978-3-030-27550-1}},
issn = {{2198-3283}},
language = {{eng}},
pages = {{147--155}},
publisher = {{Springer}},
series = {{Mathematics in Industry}},
title = {{Cyclic Structure Induced by Load Fluctuations in Adaptive Transportation Networks}},
url = {{http://dx.doi.org/0.1007/978-3-030-27550-1_19}},
doi = {{0.1007/978-3-030-27550-1_19}},
volume = {{30}},
year = {{2019}},
}