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.
Stochastic food-chain model, stationary distribution, global asymptotic stability
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