Efeitos de ruídos sobre a formação de padrões em um sistema presa-predador discreto

Abstract

The Turing pattern formation in population dynamics is characterized by the destabilization of the homogeneous equilibrium distribution by the diffusive movement of the individuals, which leads to a heterogeneous distribution of the species in the space. The conditions on the model parameters for the pattern formation are presented for continuous as well as for Coupled Map Lattice discrete models. The conditions for diffusive instability for discrete models are applied to a spatially structured predator-prey model. In this model the prey population presents an Allee effect. The patterns resulting from this dynamics are illustrated through numerical simulations. Since the population growth can be affected by stochastic fluctuations, we introduced a density dependent demographic white noise in the prey population and analyzed its effects on the spatio-temporal distribution of the populations. We found different results depending on the movement and dynamical parameters. In general, we observed that the patterns obtained in the parameters region where the coexistence equilibrium is unstable are kept for amplitude sufficiently small.