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- Type of Document: M.Sc. Thesis
- Language: Farsi
- Document No: 42074 (02)
- University: Sharif University of Technology
- Department: Mathematical Sciences
- Advisor(s): Hesaraki, Mahmoud
- Abstract:
- Consider the following Two Reaction-Diffusion System with Predator-Prey interactions.
{ █(ut = Du Δu + f (u) "" bϕ(u)v x ∈ Ω ,t>0 ,@ @vt = Dv Δv + g(v) + cϕ(u)v x ∈ Ω ,t>0 ,)┤
The main purposes of Thesis are as follow: The effect of a protection zone in the diffusive Leslie predator–prey model, Non-existence of non-constant positive steady states of two Holling type-II predator–prey systems: Strong interaction case, In the first chapter, my work is devoted to investigate the change of behavior of diffusive Leslie predator–prey model with large intrinsic predator growth rate, when a simple protection zone Ω_0 for the prey is introduced. In other word, the existence of a critical patch size of the protection zone is shown by the means of first Dirichlet Eigenvalue of the Laplacian over Ω_0 and the intrinsic growth rate of the prey, so that there is fundamental change of the dynamical behavior of the model only when Ω_0 is above the critical patch size. For this purpose, a standard boundary blow-up problem, and classical or degenerate logistic equations are used. In the next chapter, the non-existence of non-constant positive steady state solutions of two reaction–diffusion predator–prey models with Holling type-II functional response is proved. The interaction between the predator and the prey is strong and the result implies that the global bifurcating branches of steady state solutions are bounded loops.
- Keywords:
- Predator-Prey Model ; Reaction-Diffusion Equation ; Holling 2 and Leslie Functional Response ; Global Bifurcation ; Positive Steady State ; Boundary Blow-Up Problem
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