Bulletin of Mathematical Biology

, Volume 57, Issue 5, pp 701–712 | Cite as

A universal bifurcation diagram for seasonally perturbed predator-prey models

  • Alessandra Gragnani
  • Sergio Rinaldi


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


Hopf Bifurcation Bifurcation Diagram Strange Attractor Period Doubling Stable Cycle 
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Copyright information

© Society for Mathematical Biology 1995

Authors and Affiliations

  • Alessandra Gragnani
    • 1
  • Sergio Rinaldi
    • 2
  1. 1.IIASALaxenburgAustria
  2. 2.CIRITAPolitecnico di MilanoMilanoItaly

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