Extinction in randomly perturbed Lotka-Volterra systems.

Fima Klebaner

Dept of Mathematics and Statistics, University of Melbourne, Australia

Abstract

Perturbation of the Lotka-Volterra system by white noise is considered. The mean and the variance of the noisy system are approximated by the perturbative expansion up to the second order. This results in the system of seven linear differential equations equations with periodic coefficients. Looping of the trajectories of the first moments is observed. This may explain the extinction of the species. The extinction occurs in region of the phase-space with the greatest randomness.