Abstract

In this work, the analysis will be based on a Leslie–Gower type predation model, described by a two-dimensional system of ordinary differential equations, assuming that the prey population is influenced by an Allee effect, which modifies classical logistic equation. The functional response will be assumed linear, prey-dependent, and monotonously increasing. In turn, the equation of growth of predators will also be considered of like-logistic type, where the environmental carrying capacity for predators is assumed proportional to the prey population size. Among the most important results obtained is that for the same set of parameters, there are different behaviors of the system solutions, since two attractor singularities can appear simultaneously. Then, populations can coexist around fixed population sizes, or the prey population can become extinct.