Populations can grow, disappear or remain in time and this depends on their birth rates, mortality, immigration and emigration. For a long time, species have disappeared and others are at the same risk if protective policies are not implemented to guarantee their survival. It is necessary to consider mathematical models that help conserve the environment. The analysis of the Rosenzweig-MacArthur model was performed considering the function that protects a fixed amount of prey. For the analytical study, the qualitative theory of the systems of differential equations is used. Considering the use of shelters by dams with the functions proposed by Maynard-Smith. It is shown that the refuge influences the stability of the only equilibrium point inside the first quadrant and produces important effects in the dynamics of the prey-prey model.

No abstract