Introducción a la dinámica lenta-rápida del sistema clásico depredador-presa

Abstract

This work of degree allows to know one of the interactions in a biological ecosystem such as predation from the point of view of mathematics. First, an introduction is established that proposes the derivation of a dynamic system of ordinary differential equations that allows describing the behavior of predation between two or more species as developed by Alfred James Lotka and Vito Volterra. Second, a classical prey-predator system is studied and a conventional solution to an autonomous system is proposed. Third, a solution to the prey-predator system is proposed using a technique called linearization. Finally, it is assumed that the birth rate of the prey is smaller compared to the death rate of the predator, which leads to the appearance of a small parameter that allows observing that the system may have some solutions with a slow-fast structure, that is, the system is transformed into two systems known as slow system and fast system, which allows constructing an approximate solution that describes the behavior of time more explicitly.