×

Existence of positive solutions for the predator-prey systems with Ivlev’s type functional response. (Chinese. English summary) Zbl 1274.35196

Summary: The steady-state problem of Ivlev’s type predator-prey systems with prey and predator both having linear density restricts is studied. The conditions for the coexistence of the two populations are obtained. Using eigenvalue theory, perturbation theory and bifurcation theory of linear operators, the bifurcation from a constant steady-state solution under a certain condition is obtained when the diffusion coefficient is used as a bifurcation parameter. Moreover, the local branch extends to a global branch and the structure near the bifurcation point is given. The result indicates that two populations can coexist with an appropriate diffusion coefficient of the predator (natural enemy).

MSC:

35K57 Reaction-diffusion equations
35B09 Positive solutions to PDEs
92D40 Ecology
35Q92 PDEs in connection with biology, chemistry and other natural sciences
PDFBibTeX XMLCite