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A dynamics research in a predator-prey system with a nonlinear growth rate. (Chinese. English summary) Zbl 1340.35156
Summary: This paper is concerned with dynamics of a predator-prey system subject to homogeneous Dirichlet boundary conditions, where the predator population reproduces by the nonlinear function $$1/(1+ev)$$. Existence and uniqueness of coexistence states for the predator-prey system are investigated. Moreover, some asymptotic behaviors of time-dependent solutions are shown and some numerical simulations are done to complement the analytical results. The main tools used here include an implicit function theorem, bifurcation theory and perturbation technique.
##### MSC:
 35K57 Reaction-diffusion equations 92D25 Population dynamics (general) 35A01 Existence problems for PDEs: global existence, local existence, non-existence 35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
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