TY - JOUR

T1 - On a competitive system with ideal free dispersal

AU - Cantrell, Robert Stephen

AU - Cosner, Chris

AU - Martínez, Salomé

AU - Torres, Nicolás

N1 - Funding Information:
R.S.C. and C.C. are supported in part by NSF Awards DMS 11-18623 and 15-14752 . S.M. and N.T. are supported by FONDECYT 1130602 , CONICYT + PIA/Concurso de Apoyo a Centros Científicos y Tecnológicos de Excelencia con Financiamiento Basal AFB170001 .
Funding Information:
R.S.C. and C.C. are supported in part by NSF Awards DMS 11-18623 and 15-14752. S.M. and N.T. are supported by FONDECYT 1130602, CONICYT + PIA/Concurso de Apoyo a Centros Cient?ficos y Tecnol?gicos de Excelencia con Financiamiento Basal AFB170001.
Funding Information:
R.S.C. and C.C. are supported in part by NSF Awards DMS 11-18623 and 15-14752. S.M. and N.T. are supported by FONDECYT 1130602, CONICYT + PIA/Concurso de Apoyo a Centros Científicos y Tecnológicos de Excelencia con Financiamiento Basal AFB170001.

PY - 2018/10/15

Y1 - 2018/10/15

N2 - 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.

AB - 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.

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U2 - 10.1016/j.jde.2018.05.008

DO - 10.1016/j.jde.2018.05.008

M3 - Article

AN - SCOPUS:85047060578

VL - 265

SP - 3464

EP - 3493

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 8

ER -