Du, Yihong

Lou, Bendong

Peng, Rui

Zhou, Maolin

2020-04

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.

Journal of Mathematical Biology, 80(5), p. 1559-1616

1432-1416

0303-6812

32006101

https://hdl.handle.net/1959.11/28555

Springer

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

Journal Article

Publication