Abstract:
The existence of positive solutions of the steady-state system is discussed for the predator-prey model between two species with functional response Holling type Ⅱ under the second boundary conditions, in which the model has shelters and the predator is partially coupled with alternative prey. A priori-estimate of the solution is given and its stability is also discussed by means of eigenvalue theory.By means of local bifurcation theory, taking the environmental accomodation of the prey population k as a bifurcation parameter, the specific form of solutions bifurcated from the positive constant solution is given, then the condition for the local stability of bifurcation solutions is also discussed by means of eigenvalue perturbation theorem and the local bifurcation solutions can also be extended to infinite by using global bifurcation theory.
