A system of partial differential equations modeling the competition for two complementary resources in flowing habitats

Feng Bin Wang*

*Corresponding author for this work

Research output: Contribution to journalJournal Article peer-review

24 Scopus citations

Abstract

This paper examines a system of reaction-diffusion equations arising from a flowing water habitat. In this habitat, one or two microorganisms grow while consuming two growth-limiting, complementary (essential) resources. For the single population model, the existence and uniqueness of a positive steady-state solution is proved. Furthermore, the unique positive solution is globally attracting for the system with regard to nontrivial nonnegative initial values. Mathematical analysis for the two competing populations is carried out. More precisely, the long-time behavior is determined by using the monotone dynamical system theory when the semi-trivial solutions are both unstable. It is also shown that coexistence solutions exist by using the fixed point index theory when the semi-trivial solutions are both (asymptotically) stable.

Original languageEnglish
Pages (from-to)2866-2888
Number of pages23
JournalJournal of Differential Equations
Volume249
Issue number11
DOIs
StatePublished - 12 2010
Externally publishedYes

Keywords

  • Coexistence
  • Competition of algaes
  • Complementary resources
  • Essential resources
  • Fixed point index
  • Flowing habitats
  • Lower solutions
  • Maximum principle
  • Monotone dynamical system
  • Upper solutions

Fingerprint

Dive into the research topics of 'A system of partial differential equations modeling the competition for two complementary resources in flowing habitats'. Together they form a unique fingerprint.

Cite this