Positive steady state solutions of a diffusive Leslie-Gower predator-prey model with Holling type II functional response and cross-diffusion | Zendy

Jun Zhou | Zendy; Chan-Gyun Kim | Zendy; Junping Shi | Zendy

Open Access

Positive steady state solutions of a diffusive Leslie-Gower predator-prey model with Holling type II functional response and cross-diffusion

Author(s) -

Jun Zhou,

Chan-Gyun Kim,

Junping Shi

Publication year - 2014

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2014.34.3875

Subject(s) - functional response , uniqueness , mathematics , steady state (chemistry) , predation , dirichlet boundary condition , energy functional , diffusion , mathematical analysis , type (biology) , boundary value problem , predator , physics , thermodynamics , ecology , chemistry , biology , paleontology

In this paper we consider a diffusive Leslie-Gower predator-prey model with Holling type II functional response and cross-diffusion under zero Dirichlet boundary condition. By using topological degree theory, bifurcation theory, energy estimates and asymptotic behavior analysis, we prove the existence, uniqueness and multiplicity of positive steady states solutions under certain conditions on the parameters.

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