Modelos matemáticos discretos para dinâmica populacional com efeito Allee e dispersão

Abstract

The main objective of this work is to analyze the spatio-temporal dynamics of species that grow and disperse in discrete stages of time. This phenomenon is described by difference equations, with scattering by diffusion coupled by a Network of Coupled Maps. We initially present a model for a single species, whose growth is affected by a strong Allee effect. We verified, through numerical simulations, that depending on the values ​​of the intrinsic growth rate considered, different patterns of growth and spatial distribution may arise. Next, we present a prey-predator model that describes the interaction between two species, a prey subject to a strong Allee effect and its predator. The dispersion was coupled to this model in the same way as for the model with a single species. Finally, we verified through numerical simulations that with the variation of the intrinsic growth rate and of the encounters between prey and predators, the populations can be distributed in the considered domain, forming different patterns and, they can tend to different types of equilibria, such as the extinction of both species, persistence of prey only, stable or oscillatory coexistence.