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2009 | 7 | 3 | 457-471
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Stochastic dynamics and mean field approach in a system of three interacting species

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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 qualitative 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 time step is considered.
  • Dipartimento di Fisica e Tecnologie Relative, Group of Interdisciplinary Physics, Università di Palermo and CNISM-INFM, Unità di Palermo, Viale delle Scienze, edificio 18, I-90128, Palermo, Italy
  • Dipartimento di Fisica e Tecnologie Relative, Group of Interdisciplinary Physics, Università di Palermo and CNISM-INFM, Unità di Palermo, Viale delle Scienze, edificio 18, I-90128, Palermo, Italy
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