On the global analysis of dynamics in a delayed regulation model with an external interference

This paper deals with the study of a family of two-dimensional map related to a discrete model of populations generation. The inverse of the map has a vanishing denominator giving rise to non-classical singularities: a non-definition line, a focal point and a prefocal line. The properties of the domain of feasible trajectories (bounded discrete trajectories having an ecological sense) and chaotic attractors are analyzed by the use of the theories of the singularities of the planar maps.