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In this thesis, a model of predator-prey with a continuous threshold harvesting with refuge and without refuge the prey is formulated; and its dynamics, also, its direct effects on ecosystem such as the stability properties of some periodic solutions and coexistence eqilibria are surveyed. Numerical and theoretical analyses are used to investigate boundedness of solutions, stability of eqilibria, periodic orbits, bifurcations and heteroclinic orbits  

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...