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

Qimin Zhang, M. Ye, H. Lei, Q. Jin

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

Keywords


resource competition, biology species system, fractional Brownian motion, persistence, extinction.



DOI: http://dx.doi.org/10.21914/anziamj.v58i0.10997



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.