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A qualitative analysis of a predator-prey model with alternative prey. (Chinese. English summary) Zbl 1340.35351
Summary: The existence of positive steady-state solutions of a two species predator-prey model, in which the predator is partially coupled with alternative prey, is investigated. By means of lower and upper solutions, a priori estimate of the non-negative steady-state solutions of the system is given. Taking the intrinsic growth rate of the prey population $$r$$ as a bifurcation parameter, the concrete form of solutions bifurcated from the positive constant solution is given by local bifurcation theory and the local bifurcation solutions can also be extended to infinite by using global bifurcation theory.
##### MSC:
 35Q92 PDEs in connection with biology, chemistry and other natural sciences 35B32 Bifurcations in context of PDEs 35K57 Reaction-diffusion equations 92D25 Population dynamics (general) 35B09 Positive solutions to PDEs
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