Moment equations in a Lotka-Volterra extended system with time correlated noise

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 den- sities 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. How- ever, 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.