Stochastic dynamics and mean field approach in a system of three interacting species |
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Authors: | Davide Valenti Bernardo Spagnolo |
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Institution: | (1) 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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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 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.
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Keywords: | statistical mechanics population dynamics noise-induced effects |
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