(untitled) (Selecciones Matemáticas, 2024)
In various previous works, different predation models have been analyzed considering the use of refuge by the prey population, without carrying out an exhaustive analysis of its dynamics. In some of them it is stated that the use of shelters or dens by a fraction of the prey population has a stabilizing effect on predator-prey interaction. One of the objectives of this work is to show that some of these new systems considering refuge may have the same topological portrait in the phase plane as the original; but in others the dynamics change strongly. In our research we will introduce modifications to the well-known Volterra model, considering various ways to express the number of prey in refuge. In several of them, local dynamics equivalent to the original model are obtained, confirming that results reported as new were previously known based on the original system, without taking into account the refuge of the prey. We conclude that the behavior of the systems depends on the mathematical expression to describe the number of sheltered prey.