Global analysis of an ecological populational model with an external interference

This paper aims at giving new results, by a computer-assisted analysis, on some global bifurcations that change structure of the domain of feasible trajectories (bounded discrete trajectories having an ecological sense). A model considering survival of adults for two breeding seasons is used to show that the domain boundaries can be obtained by the union of all rank preimages of axes of the plane. This model belongs to a non-invertible map, and it is investigated by the use of critical curves, a powerful tool for the analysis of global properties of two-dimensional maps. The basins of attraction are obtained by numerical explorations namely the classical method of scanning pixel by pixel. The results illustrate that the basin boundary may also be contained in the union of all the preimages of the two axes. Furthermore, the differences and relations between the domains and the basins are presented.