HOPF Bifurcation in Host-Parasitoid Models

摘要

A host-parasitoid model of generation n with explicit Arnold normal form is studied. The fact that the Hopf bifurcation, the shape, and size of the elliptic limit curve can be derived in terms of the parameter of the model is proved. The fact that models have a rich bifurcation behavior with both forward and backward Hopf bifurcations and with a transition zone in the parameter for which there exists a pair of limit curves, one stable and one unstable, is revealed by numerical experiments.