On a competitive system with ideal free dispersal

Robert Stephen Cantrell, Chris Cosner, Salomé Martínez, Nicolás Torres

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

In this article we study the long term behavior of the competitive system {[Formula presented]=∇⋅[α(x)∇[Formula presented]]+u(m(x)−u−bv)inΩ,t>0,[Formula presented]=∇⋅[β(x)∇v]+v(m(x)−cu−v)inΩ,t>0,∇[Formula presented]⋅nˆ=∇v⋅nˆ=0on∂Ω,t>0, which supports for the first species an ideal free distribution, that is a positive steady state which matches the per-capita growth rate. Previous results have stated that when b=c=1 the ideal free distribution is an evolutionarily stable and neighborhood invader strategy, that is the species with density v always goes extinct. Thus, of particular interest will be to study the interplay between the inter-specific competition coefficients b,c and the diffusion coefficients α(x) and β(x) on the critical values for stability of semi-trivial steady states, and the structure of bifurcation branches of positive equilibria arising from these equilibria. We will also show that under certain regimes the system sustains multiple positive steady states.

Original languageEnglish (US)
Pages (from-to)3464-3493
Number of pages30
JournalJournal of Differential Equations
Volume265
Issue number8
DOIs
StatePublished - Oct 15 2018

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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