Diffusive Predator-prey System in Heterogeneous Environment with Harvesting of Prey

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Shabani Rokn Vafa, Saeed | 2013

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Type of Document: Ph.D. Dissertation
Language: Farsi
Document No: 45873 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Fotouhi , Morteza; Torabi Tehrani, Hossein
Abstract:
In this thesis, we study diffusive heterogeneous predator-prey system with Holling type-II functional response in the presence of harvesting in prey equation i.e.8>>>>><>>>>>: Δu = u a(x)u2 buv1 + mu ch(x) inΩ;Δv = v v2 +duv1 + muinΩ;@u = @v = 0 on @Ω,where Ω is a smooth bounded region in RN and a(x) is a nonnegative continuous function on Ω, with Ω0 a region such that Ω0 Ω and a(x) > 0on ΩnΩ0. We show that in the case of weak prey growth rate, i.e. less than the first eigenvalue of Δ in Ω0 with Dirichlet boundary condition,the system has a positive solution for the values of in a bounded interval and c > 0 sufficiently small. We also investigate the multiplicity of positive solutions in this case. When the prey growth rate is strong, we will show that the system has a positive solution for large positive value of , again provided
that c is sufficiently small
Keywords:
Predator-Prey System ; Fisheries ; Degree Theory ; Bifurcation

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