Um estudo sobre a resposta funcional em modelos discretos presa predador

Abstract

In this work, we formulated four discrete prey-predator models to analyze the effects of Functional Response on the dynamics and spatial distribution of preys and predators. We consider that, in the absence of the predator, the prey grows according to the BevertonHolt model. We consider that predation is described by the following Functional Responses: Holling Type I, Holling Type II, Holling Type III and in the fourth model, the functional response of Angelis and Beddington, for which we show a different interpretation to that originally proposed, presented by Geritz and Gyllenberg. In each of the models we look for equilibrium solutions, as well as the region of stability of these solutions. After studying the local dynamics of each model, we included a spatial variable in the models. Therefore, the difference equations are coupled by dispersion in Coupled Map Lattices. Using the same values for the local dynamical parameters and adding values for the diffusion coefficients of prey and predators, we sought to verify the influence of species movement through numerical simulations in the Wolfran Mathematica software.