Cyclic Structure Induced by Load Fluctuations in Adaptive Transportation Networks

Erik Andreas Martens, Konstantin Klemm

Research output: Chapter in Book/Report/Conference proceedingBook chapterResearchpeer-review

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.
Original languageEnglish
Title of host publicationProgress in Industrial Mathematics at ECMI 2018
EditorsI. Faragó , F. Izsák , P. Simon
Number of pages9
PublisherSpringer
Publication date2019
Pages147-155
ISBN (Print)978-3-030-27549-5
DOIs
Publication statusPublished - 2019
EventEuropean Consortium for Mathematics in Industry 2018 - Danubius Health And Spa Resort Hotel Helia, Budapest , Hungary
Duration: 18 Jun 201822 Jun 2018

Conference

ConferenceEuropean Consortium for Mathematics in Industry 2018
LocationDanubius Health And Spa Resort Hotel Helia
CountryHungary
CityBudapest
Period18/06/201822/06/2018
SeriesMathematics in Industry
Volume30

Cite this

Martens, E. A., & Klemm, K. (2019). Cyclic Structure Induced by Load Fluctuations in Adaptive Transportation Networks. In I. Faragó , F. Izsák , & P. Simon (Eds.), Progress in Industrial Mathematics at ECMI 2018 (pp. 147-155). Springer. Mathematics in Industry, Vol.. 30 https://doi.org/10.1007/978-3-030-27550-1_19