The nonlinear analysis on a discrete host-parasitoid model with pesticidal interference

A host-parasitoid model with a pesticidal interference is investigated. The global bifurcations of feasible sets and domains, caused by pesticide-related mortality, are given in the light of some recent results on iterated maps with vanishing denominator giving rise to non-classical singularities: a non-definition line, a focal point and a prefocal line. In particular, we give an answer to one of the open problems proposed by Kocic and Ladas.