uu.seUppsala University Publications
Change search
ReferencesLink to record
Permanent link

Direct link
Current-reinforced random walks for constructing transport networks
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics. (collective behaviour)
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
Show others and affiliations
2013 (English)In: Journal of the Royal Society Interface, ISSN 1742-5662, E-ISSN 1742-5689, Vol. 10, no 80, 20120864- p.Article in journal (Refereed) Published
Abstract [en]

Biological systems that build transport networks, such as trail-laying ants and the slime mould Physarum, can be described in terms of reinforced random walks. In a reinforced random walk, the route taken by 'walking' particles depends on the previous routes of other particles. Here, we present a novel form of random walk in which the flow of particles provides this reinforcement. Starting from an analogy between electrical networks and random walks, we show how to include current reinforcement. We demonstrate that current-reinforcement results in particles converging on the optimal solution of shortest path transport problems, and avoids the self-reinforcing loops seen in standard density-based reinforcement models. We further develop a variant of the model that is biologically realistic, in the sense that the particles can be identified as ants and their measured density corresponds to those observed in maze-solving experiments on Argentine ants. For network formation, we identify the importance of nonlinear current reinforcement in producing networks that optimize both network maintenance and travel times. Other than ant trail formation, these random walks are also closely related to other biological systems, such as blood vessels and neuronal networks, which involve the transport of materials or information. We argue that current reinforcement is likely to be a common mechanism in a range of systems where network construction is observed.

Place, publisher, year, edition, pages
2013. Vol. 10, no 80, 20120864- p.
National Category
Other Mathematics
URN: urn:nbn:se:uu:diva-187306DOI: 10.1098/rsif.2012.0864ISI: 000314285400014OAI: oai:DiVA.org:uu-187306DiVA: diva2:574198
Available from: 2012-12-04 Created: 2012-12-04 Last updated: 2013-03-04Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full text

Search in DiVA

By author/editor
Ma, QiSumpter, David
By organisation
Analysis and Applied MathematicsDepartment of Mathematics
In the same journal
Journal of the Royal Society Interface
Other Mathematics

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 179 hits
ReferencesLink to record
Permanent link

Direct link