Positive solutions for a general Gause-type predator-prey model with monotonic functional response. (English) Zbl 1226.92072
Summary: We study a general Gause-type predator-prey model with monotonic functional response under Dirichlet boundary conditions. Necessary and sufficient conditions for the existence and nonexistence of positive solutions for this system are obtained by means of the fixed point index theory. In addition, the local and global bifurcations from a semitrivial state are also investigated on the basis of bifurcation theory. The results indicate that diffusion and functional response helps to create stationary patterns.
MSC:
| 92D40 | Ecology |
| 35B32 | Bifurcations in context of PDEs |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 35J25 | Boundary value problems for second-order elliptic equations |
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