Stochastic dynamics and mean field approach in a system of three interacting species

Abstract

The spatio-temporal dynamics of three interacting species, two preys and one predator, in the presence of two different kinds of noise sources is studied. To describe the spatial distributions of the species we use a model based on Lotka-Volterra equations. A correlated dichotomous noise acts on β, the interaction parameter between the two preys, and a multiplicative white noise affects directly the dynamics of each one of the three species. We study the time behaviour of the three species in single site for different values of the multiplicative noise intensity, finding noise-induced oscillations of the three species densities with an anticorrelated behaviour of the two preys. Afterwards, by considering a spatially extended system formed by a two-dimensional lattice with N sites and applying a mean field approach, we get the corresponding moment equations in Gaussian approximation. Within this formalism we obtain the time behaviour of the first and second order moments for different values of multiplicative noise intensity, with β(t) subject to the same dichotomous noise source. Finally, we compare our results with those obtained by using a coupled map lattice model, consisting of a time discrete version of the Lotka-Volterra equations.

21 pages, 7 figures. Submitted to Centr. Eur. J. Phys

References in corpus (4)

• Correlated noise in a logistic growth model
• Environmental Metal Pollution Considered as Noise: Effects on the Spatial Distribution of Benthic Foraminifera in two Coastal Marine Areas of Sicily (Southern Italy)
• Nonmonotonic Behavior of Spatiotemporal Pattern Formation in a Noisy Lotka-Volterra System
• Macroscopic limit cycle via pure noise-induced phase transition