Effects of dispersal for a predator-prey model in a heterogeneous environment. (English) Zbl 1481.35179
Summary: In this paper, we study the stationary problem of a predator-prey cross-diffusion system with a protection zone for the prey. We first apply the bifurcation theory to establish the existence of positive stationary solutions. Furthermore, as the cross-diffusion coefficient goes to infinity, the limiting behavior of positive stationary solutions is discussed. These results implies that the large cross-diffusion has beneficial effects on the coexistence of two species. Finally, we analyze the limiting behavior of positive stationary solutions as the intrinsic growth rate of the predator species goes to infinity.
MSC:
| 35J57 | Boundary value problems for second-order elliptic systems |
| 92D25 | Population dynamics (general) |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
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