Asymptotic behaviour of a class of resource competition biology species system by the fractional Brownian motion

Abstract

We analyse the asymptotic behaviour of a biological system described by a stochastic competition model with \(n\) species and \(k\) resources (chemostat model), in which the species mortality rates are influenced by the fractional Brownian motion of the extrinsic noise environment. By constructing a Lyapunov functional, the persistence and extinction criteria are derived in the mean square sense. Some examples are given to illustrate the effectiveness of the theoretical result. doi:10.1017/S1446181117000098