Moment equations in a system of three interacting species subject to colored noise

We study the effects of the colored noise on a Lotka-Volterra system of three interacting species, namely two preys and one predator, in a two-dimensional domain. The three species are affected by an external multiplicative time correlated noise, which accounts for environment fluctuations. Moreover, the interaction parameter between the two preys is a dichotomous stochastic process, which determines two dynamical regimes corresponding to different biological conditions. First, we study the noise effects on the three species dynamics in a single site. Afterwards, by a mean field approach we obtain, in Gaussian approximation, the moment equations for the species densities. Within this formalism we analyze the effect of the external colored noise on the spatially extended system. We find that the multiplicative noise does not affect the time behavior of the 1st order moments. Conversely, the 2nd order moments are strongly dependent both on the intensity and correlation time of the multiplicative noise. Finally, we compare our results with those obtained by a discrete time approach based on a model of coupled map lattice.