Limit cycles in predator-prey models.

The general model of interaction between one predator and one prey is studied. A unimodal function of rate of growth of the prey and concave down functional response of the predator is assumed. In this work it is shown that for a given natural number n there exist models possessing at least 2n + 1 limit cycles. It is also proved, applying the Hopf bifurcation theorem, that a model exists with a logistic growth rate of the prey and concave down functional response that has at least two limit cycles.