| Abstract: |
| Because generalist predators feed on the most abundant prey species, they can persist even if one prey species is absent. Predation by generalist predators is typically characterized by Holling`s type III functional response, so that predation pressure for a given prey species is small when the density of that prey is low. Hanski et al. have suggested that specialist predators contribute to population cycles while generalist predators have a stabilizing effect. Almost none of existing predator-prey models considers alternative food sources for the generalist predator. In particular, in these models, the generalist predator goes extinct in the absence of the one focal prey. We model the dynamics of a generalist predator with a type III (sigmoidal) functional response on one dynamic prey and fixed alternative food source. We find that the system has at most six equilibria and it can exhibit bistability, limit cycles and several global bifurcations. |
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