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Qualitative analysis of a predator--prey model with Holling type II functional response incorporating a prey refuge. (English) Zbl 05115330
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.

35J60Nonlinear elliptic equations
92D25Population dynamics (general)
Full Text: DOI
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