This paper intends to study some dynamical properties of a stochasticthree-dimensional Lotka--Volterra system. Under some mild assumptions, we first introduce a simple method to show thatthe model has a global and positive solution almost surely. Secondly,we prove that this model has a stationary distribution. Then we study the global asymptoticstability of the positive solution. Finally, some numerical simulations are introduced toillustrate the theoretical results.
QIU, HONG and DENG, WENMIN
"Stationary distribution and global asymptotic stability of a three-species stochastic food-chain system,"
Turkish Journal of Mathematics: Vol. 41:
5, Article 18.
Available at: https://journals.tubitak.gov.tr/math/vol41/iss5/18