A UNIVERSAL BIFURCATION DIAGRAM FOR SEASONALLY PERTURBED PREDATOR-PREY MODELS

The bifurcations of a periodically forced predator-prey model (the che mostat model), with a prey feeding on a limiting nutrient, are numeric ally detected with a continuation technique. Eight bifurcation diagram s are produced (one for each parameter in the model) and shown to be t opologically equivalent. These diagrams are also equivalent to those o f the most commonly used predator-prey model (the Rosenzweig-McArthur model). Thus, all basic modes of behavior of the two main predator-pre y models can be explained by means of a single bifurcation diagram.