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

D. Valenti·L. Schimansky-Geier·X. Sailer·B. Spagnolo·M. Iacomi
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Abstract

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 $1^{st}$ order moments are independent on the multiplicative noise source. However the behavior of the $2^{nd}$ 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.

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D. Valenti, L. Schimansky-Geier, X. Sailer, B. Spagnolo, M. Iacomi. 2006-11-14. Moment equations in a Lotka-Volterra extended system with time correlated noise. https://arxiv.org/abs/cond-mat/0611358

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