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.