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Existence and asymptotic behavior of solutions for a predator-prey system with a nonlinear growth rate. (English) Zbl 1387.35365
Summary: The paper is concerned with a predator-prey diffusive system subject to homogeneous Neumann boundary conditions, where the growth rate \((\frac{\alpha}{1+\beta v})\) of the predator population is nonlinear. We study the existence of equilibrium solutions and the long-term behavior of the solutions. The main tools used here include the super-sub solution method, the bifurcation theory and linearization method.

MSC:
35K57 Reaction-diffusion equations
35B35 Stability in context of PDEs
35Q92 PDEs in connection with biology, chemistry and other natural sciences
92D25 Population dynamics (general)
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