On the impulsive Beverton-Holt equation and extinction conditions in population dynamics

This paper is devoted to investigate extinction and non-extinction conditions of the extended Beverton-Holt equation for dynamics of populations in Ecology when potential discontinuities at sampling points are included in the model. Such discontinuities are related to impulses in the corresponding continuous-time logistic equation. The discontinuities are parameterized by two sequences of parameters, namely, the harvesting (i.e. the hunting or fishing quota) and the internal consumption which can include positive and negative migrations in the considered population habitat.