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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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