A spatially extended Lotka-Volterra system of two competing species in the
presence of two correlated noise sources is analyzed: (i) an external
multiplicative time correlated noise, which mimics the interaction between the
system and the environment; (ii) a dichotomous stochastic process, whose jump
rate is a periodic function, which represents the interaction parameter between
the species. The moment equations for the species densities are derived in
Gaussian approximation, using a mean field approach. Within this formalism we
study the effect of the external time correlated noise on the ecosystem
dynamics. We find that the time behavior of the 1st order moments are
independent on the multiplicative noise source. However the behavior of the
2nd order moments is strongly affected both by the intensity and the
correlation time of the multiplicative noise. Finally we compare our results
with those obtained studying the system dynamics by a coupled map lattice
model.Comment: 12 pages, 7 figures, to appear in Acta Phys. Pol.