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. 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, it is proved that the model bifurcations at the point (d(j)2,(u*,v*)). In the one dimensional case, by means of global bifurcation theory, it is proved that the local bifurcation at (d(j)2,(u*,v*)) can be extended to global bifurcation, and the continuum τj joins up with infinity.
