Stationary distribution and global asymptotic stability of a three-species stochastic food-chain system

Authors

HONG QIU
WENMIN DENG

Abstract

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.

DOI

10.3906/mat-1510-52

Keywords

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

First Page

1292

Last Page

1307

Recommended Citation

QIU, H, & DENG, W (2017). Stationary distribution and global asymptotic stability of a three-species stochastic food-chain system. Turkish Journal of Mathematics 41 (5): 1292-1307. https://doi.org/10.3906/mat-1510-52