Bifurcations in discontinuous mathematical models with control strategy for a species.

In this paper a preliminary mathematical model is proposed, by means of a system of ordinary differential equations, for the growth of a species. In this case, the species does not interact with another species and is divided into two stages, those that have or have not reached reproductive maturity, with natural and control mortality for both stages. When performing a qualitative analysis to determine conditions in the parameters that allow the extinction or preservation of the species, a modification is made to the model when only control is assumed for each of the stages if the number of species in that stage is above a critical value. These studies are carried out by bifurcation analysis with respect to two parameters: control for each stage and their critical values. It is concluded that for certain conditions in their parameters, the dynamics in each of the controlled stages converge to their critical values.