Please use this identifier to cite or link to this item: https://hdl.handle.net/1959.11/28555
Title: The Fisher-KPP equation over simple graphs: varied persistence states in river networks
Contributor(s): Du, Yihong  (author)orcid ; Lou, Bendong (author); Peng, Rui (author); Zhou, Maolin  (author)
Publication Date: 2020-04
Early Online Version: 2020-01-31
DOI: 10.1007/s00285-020-01474-1
Handle Link: https://hdl.handle.net/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.
Publication Type: Journal Article
Grant Details: ARC/DP190103757
Source of Publication: Journal of Mathematical Biology, 80(5), p. 1559-1616
Publisher: Springer
Place of Publication: Germany
ISSN: 1432-1416
0303-6812
Fields of Research (FoR) 2008: 010110 Partial Differential Equations
010202 Biological Mathematics
Fields of Research (FoR) 2020: 490410 Partial differential equations
490102 Biological mathematics
Socio-Economic Objective (SEO) 2008: 970101 Expanding Knowledge in the Mathematical Sciences
Socio-Economic Objective (SEO) 2020: 280118 Expanding knowledge in the mathematical sciences
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
Appears in Collections:Journal Article
School of Science and Technology

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