Abstract:
A predator-prey diffusion model in heterogeneous environment is researched.For the case of weak growth of prey, the existence of positive solutions are obtained near two semi-trivial solutions by using the bifurcation theory; moreover, the global structure are given. Secondly, for the case of strong growth of prey, the sufficient conditions:λ∈(0,min{λD1(Ω0),1/m3}),μ∈λm11-λm3,M for the existence of positive solutions are showed by the degree theory and the regular perturbation theory. Considering the spatial heterogeneity and the influence of the degradation factor, some simulations are done in order to verify the theoretical results.
