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 Volume 10, Number 4, 2020, Pages 1464-1481 Dynamics of a stochastic chemostat competition model with plasmid-bearing and plasmid-free organisms Miaomiao Gao,Daqing Jiang,Tasawar Hayat,Ahmed Alsaedi,Bashir Ahmad Keywords:Stochastic chemostat model, plasmid-bearing, plasmid-free, stationary distribution. Abstract: In this paper, we consider a chemostat model of competition between plasmid-bearing and plasmid-free organisms, perturbed by white noise. Firstly, we prove the existence and uniqueness of the global positive solution. Then by constructing suitable Lyapunov functions, we establish sufficient conditions for the existence of a unique ergodic stationary distribution. Furthermore, conditions for extinction of plasmid-bearing organisms are obtained. Theoretical analysis indicates that large noise intensity $\sigma_{2}^{2}$ is detrimental to the survival of plasmid-bearing organisms and is not conducive to the commercial production of genetically altered organisms. Finally, numerical simulations are presented to illustrate the results. PDF      Download reader