Population dynamics in river networks: analysis of steady states View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-04-02

AUTHORS

Olga Vasilyeva

ABSTRACT

We study the population dynamics of an aquatic species in a river network. The habitat is viewed as a binary tree-like metric graph with the population density satisfying a reaction-diffusion-advection equation on each edge, along with the appropriate junction and boundary conditions. In the case of a linear reaction term and hostile downstream boundary condition, the question of persistence in such models was studied by Sarhad, Carlson and Anderson. We focus on the case of a nonlinear (logistic) reaction term and use an outflow downstream boundary condition. We obtain necessary and sufficient conditions for the existence and uniqueness of a positive steady state solution for a simple Y-shaped river network (with a single junction). We show that the existence of a positive steady state is equivalent to the persistence condition for the linearized model. The method can be generalized to a binary tree-like river network with an arbitrary number of segments. More... »

PAGES

1-38

References to SciGraph publications

  • 2010-11. Population persistence in the face of advection in THEORETICAL ECOLOGY
  • 2012-11. Population persistence under advection–diffusion in river networks in JOURNAL OF MATHEMATICAL BIOLOGY
  • 2014-08. Population persistence in river networks in JOURNAL OF MATHEMATICAL BIOLOGY
  • 2009-07. Phytoplankton depth profiles and their transitions near the critical sinking velocity in JOURNAL OF MATHEMATICAL BIOLOGY
  • 2014-12. Evolution of dispersal in open advective environments in JOURNAL OF MATHEMATICAL BIOLOGY
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00285-019-01350-7

    DOI

    http://dx.doi.org/10.1007/s00285-019-01350-7

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1113179858

    PUBMED

    https://www.ncbi.nlm.nih.gov/pubmed/30941507


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