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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) ; 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 |
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Appears in Collections: | Journal Article School of Science and Technology |
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