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

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6 Citations (Scopus)

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, by using Lotka-Volterra equations. A correlated dichotomous noise acts on the interaction parameter between the two preys, and a multiplicative white noise affects directly the dynamics of the three species. After analyzing the time behaviour of the three species in a single site, we consider a two-dimensional spatial domain, applying a mean field approach and obtaining the time behaviour of the first and second order moments for different multiplicative noise intensities. We find noise-induced oscillations of the three species with an anticorrelated behaviour of the two preys. Finally, we compare our results with those obtained by using a coupled map lattice (CML) model, finding a good ualitative agreement. However, some quantitative discrepancies appear, that can be explained as follows:i) different stationary values occur in the two approaches; ii) in the mean field formalism the interaction between sites is extended to the whole spatial domain, conversely in the CML model the species interaction is restricted to the nearest neighbors; iii) the dynamics of the CML model is faster since an unitary timestep is considered.
Original languageEnglish
Pages (from-to)457-471
Number of pages15
JournalCentral European Journal of Physics
Volume7
Publication statusPublished - 2009

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy

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