Spatial heterogeneity of resources versus lotka-volterra dynamics

V. Hutson, Y. Lou, K. Mischaikow

Research output: Contribution to journalArticlepeer-review

62 Scopus citations

Abstract

The problem is motivated by a consideration of two phenotypes of a species in a strongly heterogenous spatial environment. The phenotypes vary in their diffusion rates and interspecific interactions. The aim is to investigate the relative strengths of the diffusion and reaction effects. The problem is thus of competing species type, but there are many questions which arise which are not covered by standard theory. We investigate, in particular, the stability of the equilibria and the existence of coexistence solutions with emphasis on cases where the spatial variation of the environment becomes large. We discuss briefly the implications of our results for the principle of competitive exclusions and for the question of the evolution of diffusion discussed in Dockery et al.

Original languageEnglish (US)
Pages (from-to)97-136
Number of pages40
JournalJournal of Differential Equations
Volume185
Issue number1
DOIs
StatePublished - Oct 10 2002
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Keywords

  • Coexistence
  • Competitive exclusion
  • Evolution of diffusion
  • Reaction-diffusion
  • Spatial heterogeneity
  • Stability

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