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Qualitative analysis of a predator-prey model with Holling type II functional response incorporating a prey refuge. (English) Zbl 1387.35588

Summary: We study a predator-prey model with Holling type II functional response incorporating a prey refuge under homogeneous Neumann boundary condition. We show the existence and non-existence of non-constant positive steady-state solutions depending on the constant \(m\in (0,1]\), which provides a condition for protecting \((1 - m)u\) of prey \(u\) from predation. Moreover, we investigate the asymptotic behavior of spacially inhomogeneous solutions and the local existence of periodic solutions.

MSC:

35Q92 PDEs in connection with biology, chemistry and other natural sciences
35J56 Boundary value problems for first-order elliptic systems
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
35J60 Nonlinear elliptic equations
92D25 Population dynamics (general)
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