The Fisher-KPP equation over simple graphs: varied persistence states in river networks

Title
The Fisher-KPP equation over simple graphs: varied persistence states in river networks
Publication Date
2020-04
Author(s)
Du, Yihong
( author )
OrcID: https://orcid.org/0000-0002-1235-0636
Email: ydu@une.edu.au
UNE Id une-id:ydu
Lou, Bendong
Peng, Rui
Zhou, Maolin
Type of document
Journal Article
Language
en
Entity Type
Publication
Publisher
Springer
Place of publication
Germany
DOI
10.1007/s00285-020-01474-1
UNE publication id
une:1959.11/28555
Abstract
In this article, we study the dynamical behaviour of a new species spreading from a location in a river network where two or three branches meet, based on the widely used Fisher-KPP advection-diffusion equation. This local river system is represented by some simple graphs with every edge a half infinite line, meeting at a single vertex. We obtain a rather complete description of the long-time dynamical behaviour for every case under consideration, which can be classified into three different types (called a trichotomy), according to the water flow speeds in the river branches, which depend crucially on the topological structure of the graph representing the local river system and on the cross section areas of the branches. The trichotomy includes two different kinds of persistence states, and the state called "persistence below carrying capacity" here appears new.
Link
Citation
Journal of Mathematical Biology, 80(5), p. 1559-1616
ISSN
1432-1416
0303-6812
Pubmed ID
32006101
Start page
1559
End page
1616

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