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

TL;DR

This paper derives and analyzes moment equations for a spatially extended Lotka-Volterra model with correlated noise, revealing how noise intensity and correlation time influence species interactions and ecosystem dynamics.

Contribution

It introduces a Gaussian approximation-based formalism to study the effects of correlated noise on a Lotka-Volterra system, extending previous models with new analytical insights.

Findings

First order moments are unaffected by multiplicative noise.

Second order moments are significantly influenced by noise intensity and correlation time.

Comparison with coupled map lattice models validates the analytical approach.

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.